Quadrant Rotations Worksheet Geometry Transformations
Rotating Figures Across Quadrants
Coordinate Plane CLASSWORK
Name:
Date:
Period:
Visual Reference & Rotation Guide
Origin (0,0) Center of Rotation
x y CCW ↺ CW ↻ Quad II (-, +) Quad I (+, +) Quad III (-, -) Quad IV (+, -)
4 Quadrants = Full 360° Circle
Rotation Paths Quick Formula
CCW (Counterclockwise):
I → II → III → IV
CW (Clockwise):
I → IV → III → II
1 Quadrant = 90° 2 Quadrants = 180° 3 Quadrants = 270° 4 Quadrants = 360°
Worked Example
Model Problem
Prompt: A CCW rotation from Quadrant I to Quadrant II .1 quadrant .
90 degrees
Independent Practice
Choose from: 90°, 180°, 270°, or 360°
Read each description carefully. Track the directional movement across quadrants and record the exact degree of rotation.
Description of Rotation
Number of Degrees
1
A CCW rotation from Quadrant I to Quadrant III.
2
A CCW rotation from Quadrant III to Quadrant IV.
3
A CCW rotation from Quadrant I to Quadrant IV.
4
A CCW rotation from Quadrant II to Quadrant II.
5
A CW rotation from Quadrant II to Quadrant IV.
6
A CW rotation from Quadrant I to Quadrant III.
7
A CW rotation from Quadrant II to Quadrant III.
8
A CW rotation from Quadrant IV to Quadrant I.
9
A CW rotation from Quadrant III to Quadrant I.
10
A CW rotation from Quadrant I to Quadrant I.
Pro Tip: 180° rotations always land in the opposite quadrant, regardless of whether you rotate CW or CCW!
Page 1 of 1
Quadrant Rotations Answer Key Teacher Edition & Solutions
Rotating Figures Across Quadrants
Answer Key
Standard: CCSS.MATH.CONTENT.8.G.A.3
Topic: Origin Rotations (90°, 180°, 270°, 360°)
Grading: 10 Points Total (1 pt each)
Reference Summary & Teacher Pointers
Coordinate Rotations Around (0,0)
x y CCW ↺ CW ↻ Quad II (-, +) Quad I (+, +) Quad III (-, -) Quad IV (+, -)
Four 90° quadrants = 360° total
Core Movement Rules Formula
CCW (↺):
I → II → III → IV
CW (↻):
I → IV → III → II
Rule: \(\text{Quadrant Steps} \times 90^\circ\) Opposite Quad = 180° always
Common Student Pitfalls
Teacher Alert
• CW vs CCW confusion: Ensure students verify direction before counting steps.Full Turn (360°): Landing in the starting quadrant indicates a full 360° turn (not 0°).
Practice Solutions with Quadrant Paths
All 10 Questions Answered
Description of Rotation
Quadrant Path / Steps
Correct Answer
1
A CCW rotation from Quadrant I to Quadrant III.
I → II → III (2 jumps)
180 degrees (180°)
2
A CCW rotation from Quadrant III to Quadrant IV.
III → IV (1 jump)
90 degrees (90°)
3
A CCW rotation from Quadrant I to Quadrant IV.
I → II → III → IV (3 jumps)
270 degrees (270°)
4
A CCW rotation from Quadrant II to Quadrant II.
II → III → IV → I → II (4 jumps)
360 degrees (360°)
5
A CW rotation from Quadrant II to Quadrant IV.
II → I → IV (2 jumps)
180 degrees (180°)
6
A CW rotation from Quadrant I to Quadrant III.
I → IV → III (2 jumps)
180 degrees (180°)
7
A CW rotation from Quadrant II to Quadrant III.
II → I → IV → III (3 jumps)
270 degrees (270°)
8
A CW rotation from Quadrant IV to Quadrant I.
IV → III → II → I (3 jumps)
270 degrees (270°)
9
A CW rotation from Quadrant III to Quadrant I.
III → II → I (2 jumps)
180 degrees (180°)
10
A CW rotation from Quadrant I to Quadrant I.
I → IV → III → II → I (4 jumps)
360 degrees (360°)
Extension Question: Ask students: "Why does rotating 90° CW yield the same quadrant as rotating 270° CCW?"
Teacher Guide
Mixed Rotations Homework Worksheet Homework Practice • Part 1
Rotating Figures Across Quadrants (HW)
Finding Rotation Degrees
Name:
Date:
Period:
Visual Reference & Rotation Guide
Origin (0,0) Center of Rotation
x y CCW ↺ CW ↻ Quad II (-, +) Quad I (+, +) Quad III (-, -) Quad IV (+, -)
4 Quadrants = Full 360° Turn
Rotation Directions Formula
CCW (Counterclockwise):
I → II → III → IV
CW (Clockwise):
I → IV → III → II
1 Quad = 90° 2 Quads = 180° 3 Quads = 270° 4 Quads = 360°
Worked Example
Model Problem
Prompt: A CCW rotation from Quadrant I to Quadrant II .1 quadrant .
90 degrees
Part 1: Identify the Degree of Rotation
Choose from: 90°, 180°, 270°, or 360°
Read each description carefully. Count the quadrant transitions in the given direction and record the total rotation degrees.
Description of Rotation
Number of Degrees
1
A CCW rotation from Quadrant II to Quadrant III.
2
A CCW rotation from Quadrant I to Quadrant IV.
3
A CCW rotation from Quadrant I to Quadrant II.
4
A CCW rotation from Quadrant II to Quadrant IV.
5
A CW rotation from Quadrant I to Quadrant IV.
6
A CW rotation from Quadrant I to Quadrant III.
7
A CW rotation from Quadrant I to Quadrant II.
8
A CW rotation from Quadrant II to Quadrant I.
9
A CW rotation from Quadrant IV to Quadrant III.
10
A CW rotation from Quadrant II to Quadrant II.
Tip: Remember CCW turns counterclockwise (\(\circlearrowleft\)) and CW turns clockwise (\(\circlearrowright\)).
Page 1 of 2
Homework Practice • Part 2
Rotating Figures Across Quadrants
Finding Image Locations
Name:
Target Quadrants: Quad I, II, III, or IV
Rotation Jump Guide & Image Location
Step Counter Guide
Quadrant II (- , +) Top-Left
Quadrant I (+ , +) Top-Right
Quadrant III (- , -) Bottom-Left
Quadrant IV (+ , -) Bottom-Right
↺ CCW: I → II → III → IV ↻ CW: I → IV → III → II
How Many Quadrants to Move? Step Key
90° Move 1 quad
180° Move 2 quads
270° Move 3 quads
360° Same quad
Worked Example
Model Problem
Prompt: A 90° CCW rotation from Quadrant I .
Quadrant II
Part 2: Identify the Location of the New Image
Write: Quadrant I, II, III, or IV
Read each description carefully. Start at the given quadrant, move the indicated degrees in the specified direction, and write the final quadrant.
Description of Rotation
Location of New Image
1
A 180° CCW rotation from Quadrant I.
2
A 90° CCW rotation from Quadrant I.
3
A 270° CCW rotation from Quadrant IV.
4
A 180° CCW rotation from Quadrant II.
5
A 360° CCW rotation from Quadrant IV.
6
A 90° CW rotation from Quadrant II.
7
A 90° CW rotation from Quadrant IV.
8
A 180° CW rotation from Quadrant III.
9
A 270° CW rotation from Quadrant II.
10
A 180° CW rotation from Quadrant I.
Double Check: Ensure your final answer indicates Quadrant I, Quadrant II, Quadrant III, or Quadrant IV.
Page 2 of 2
Mixed Rotations Homework Key Teacher Answer Key • Part 1
Rotating Figures Across Quadrants
HW Key • Part 1
Assignment: Mixed Homework - Part 1
Target Skill: Degree Measurement from Quadrants
Grading: 10 Points (1 pt each)
Reference Summary & Step Counting
Center of Rotation (0,0)
x y CCW ↺ CW ↻ Quad II (-, +) Quad I (+, +) Quad III (-, -) Quad IV (+, -)
Opposite Quadrants = 180°
Counting Directional Quadrants Formula
CCW Order (↺):
I → II → III → IV
CW Order (↻):
I → IV → III → II
Multiply quadrant transitions by 90°: 1=90°, 2=180°, 3=270°, 4=360°.
Key Concept: If the starting and ending quadrant are the same (e.g., #10), it represents a full rotation of 360° .
Part 1 Solutions with Quadrant Paths
Items 1–10
Description of Rotation
Quadrant Path
Correct Answer
1
A CCW rotation from Quad II to Quad III.
II → III (1 jump)
90 degrees (90°)
2
A CCW rotation from Quad I to Quad IV.
I → II → III → IV (3 jumps)
270 degrees (270°)
3
A CCW rotation from Quad I to Quad II.
I → II (1 jump)
90 degrees (90°)
4
A CCW rotation from Quad II to Quad IV.
II → III → IV (2 jumps)
180 degrees (180°)
5
A CW rotation from Quad I to Quad IV.
I → IV (1 jump)
90 degrees (90°)
6
A CW rotation from Quad I to Quad III.
I → IV → III (2 jumps)
180 degrees (180°)
7
A CW rotation from Quad I to Quad II.
I → IV → III → II (3 jumps)
270 degrees (270°)
8
A CW rotation from Quad II to Quad I.
II → I (1 jump)
90 degrees (90°)
9
A CW rotation from Quad IV to Quad III.
IV → III (1 jump)
90 degrees (90°)
10
A CW rotation from Quad II to Quad II.
II → I → IV → III → II (4 jumps)
360 degrees (360°)
Teacher Answer Key Page 1 of 2
Teacher Answer Key • Part 2
Rotating Figures Across Quadrants
HW Key • Part 2
Assignment: Mixed Homework - Part 2
Target Skill: Locating Final Quadrant Image
Grading: 10 Points (1 pt each)
Degree to Step Rules & Verification
Navigation Quick Reference
Quadrant II (- , +) Top-Left
Quadrant I (+ , +) Top-Right
Quadrant III (- , -) Bottom-Left
Quadrant IV (+ , -) Bottom-Right
↺ CCW: I → II → III → IV ↻ CW: I → IV → III → II
Step Conversion Quick-Check Reference
90° 1 step
180° 2 steps
270° 3 steps
360° 4 steps
Teacher Note: Remind students that 180° rotations in either direction yield the exact same opposite quadrant (e.g. #1, #4, #8, #10).
Part 2 Solutions with Target Quadrants
Items 1–10
Description of Rotation
Movement Steps
Location of New Image
1
A 180° CCW rotation from Quad I.
I → II → III (2 CCW)
Quadrant III
2
A 90° CCW rotation from Quad I.
I → II (1 CCW)
Quadrant II
3
A 270° CCW rotation from Quad IV.
IV → I → II → III (3 CCW)
Quadrant III
4
A 180° CCW rotation from Quad II.
II → III → IV (2 CCW)
Quadrant IV
5
A 360° CCW rotation from Quad IV.
Full circle → Quad IV (4 CCW)
Quadrant IV
6
A 90° CW rotation from Quad II.
II → I (1 CW)
Quadrant I
7
A 90° CW rotation from Quad IV.
IV → III (1 CW)
Quadrant III
8
A 180° CW rotation from Quad III.
III → II → I (2 CW)
Quadrant I
9
A 270° CW rotation from Quad II.
II → I → IV → III (3 CW)
Quadrant III
10
A 180° CW rotation from Quad I.
I → IV → III (2 CW)
Quadrant III
Teacher Answer Key Page 2 of 2
Quadrant Rotations Exit Ticket Exit Ticket
Quadrant Rotations Quick Check
Show your understanding of angle rotations around the origin.
Name:
Period:
A figure starts in Quadrant II and rotates CW into Quadrant III . What degree rotation occurred?
Choose from: 90°, 180°, 270°, or 360°
A figure in Quadrant III undergoes a 90° CCW rotation. What is the location of the new image?
Choose from: Quad I, II, III, or IV
3. Error Analysis: Nicolas claims that rotating a figure 180° CW produces a different image location than rotating it 180° CCW.
Is Nicolas correct? YES NO
Explain why:
Quick Reference Quad II (-,+) Quad I (+,+) Quad III (-,-) Quad IV (+,-)
↺ CCW: I → II → III → IV
How confident do you feel?
1 😕 2 🤔 3 🙂 4 🌟
Formative Assessment • Score: _____ / 3
Cut here for 2 half-sheet copies
Exit Ticket
Quadrant Rotations Quick Check
Show your understanding of angle rotations around the origin.
Name:
Period:
A figure starts in Quadrant II and rotates CW into Quadrant III . What degree rotation occurred?
Choose from: 90°, 180°, 270°, or 360°
A figure in Quadrant III undergoes a 90° CCW rotation. What is the location of the new image?
Choose from: Quad I, II, III, or IV
3. Error Analysis: Nicolas claims that rotating a figure 180° CW produces a different image location than rotating it 180° CCW.
Is Nicolas correct? YES NO
Explain why:
Quick Reference Quad II (-,+) Quad I (+,+) Quad III (-,-) Quad IV (+,-)
↺ CCW: I → II → III → IV
How confident do you feel?
1 😕 2 🤔 3 🙂 4 🌟
Formative Assessment • Score: _____ / 3
Quadrant Rotations Ticket Key Teacher Key
Exit Ticket Solutions & Model Answers
Quick-check formative assessment answer key for classroom grading.
Total: 3 Points
Starts in Quad II , rotates CW into Quad III :
270 degrees (270°)
Path: II → I → IV → III (3 clockwise jumps \(\times 90^\circ = 270^\circ\))
In Quad III , rotates 90° CCW :
Quadrant IV
Path: III → IV (1 counterclockwise jump of 90°)
3. Error Analysis: Nicolas claims 180° CW produces a different location than 180° CCW.
Correct Decision: YES NO (1 pt)
Acceptable Student Explanation (1 pt): "Rotating 180° is always 2 quadrant steps in either direction, so it always lands in the opposite quadrant."
Quick Scoring Guide
Q1 (1 pt): 270°
Q2 (1 pt): Quad IV
Q3 (1 pt): NO + Reason
Give half credit for Q3 if student circles NO without explanation.
Mastery Benchmark: 3 out of 3 points (100%)
Formative Assessment Rubric & Action Plan
Student Mastery Rubric & Next Instructional Steps
Group students based on score to deliver targeted follow-up instruction.
Formative Data Action Plan
3 / 3 Points Mastery
Demonstrates complete fluency determining rotation degrees, navigation paths, and quadrant symmetry.
Next Step: Assign coordinate transformation algebraic rules: \((x, y) \to (-y, x)\).
2 / 3 Points Approaching
Understands quadrant jumps but made a minor error in directional counting (CW vs CCW) or explanation.
Next Step: Quick warm-up review on finger-tracing directional arrows on coordinate plane.
0 – 1 Points Needs Support
Struggles to connect 90° intervals to quadrant shifts or confuses clockwise with counterclockwise order.
Next Step: Small-group tactile manipulatives using physical quadrant spinners.
Targeted Intervention Strategies for Common Mistakes:
• Error on Q1 (Answered 90° instead of 270°): Student counted CCW instead of CW. Have student draw a clockwise circle before tracing.
• Error on Q3 (Believes CW vs CCW is different for 180°): Have student trace both paths on the quadrant map to see they meet at the same quadrant.
Quadrant Rotations Assessment Guide • Page 1 of 1
Standard Form Study Guide Algebra 1 • Unit 2 Review
Standard Form & Intercepts Study Guide
\(Ax + By = C\)
Name:
Class/Period:
Date:
Concept Anchor: The Cover-Up Method for Intercepts
Standard Form: \(Ax + By = C\)
To find the x-intercept:
Substitute \(y = 0\) (cover \(By\)) and solve for \(x\).
Written as: \((x, 0)\)
To find the y-intercept:
Substitute \(x = 0\) (cover \(Ax\)) and solve for \(y\).
Written as: \((0, y)\)
Model: \(2x + 4y = 8\)
• \(x\)-int: \(2x = 8 \implies x = 4 \implies (4, 0)\)
Part 1: Find the x- and y-intercepts of each equation
Show substitution work
1. \(x + y = 7\)
\(x\)-int: ___________
\(y\)-int: ___________
2. \(x - 3y = 9\)
\(x\)-int: ___________
\(y\)-int: ___________
3. \(2x + 3y = -6\)
\(x\)-int: ___________
\(y\)-int: ___________
4. \(-4x - 2y = -8\)
\(x\)-int: ___________
\(y\)-int: ___________
5. \(5x - 4y = -12\)
\(x\)-int: ___________
\(y\)-int: ___________
6. \(-2x + 7y = 11\)
\(x\)-int: ___________
\(y\)-int: ___________
Part 2: Plot the given intercepts and draw the line
Large Grid (-10 to +10) • Connect with arrows
7. \(x\)-int: 4 , \(y\)-int: 5
x y 5 10 -5 -10 5 10 -5 -10
Plot \((4, 0)\) and \((0, 5)\)
8. \(x\)-int: -3 , \(y\)-int: 1
x y 5 10 -5 -10 5 10 -5 -10
Plot \((-3, 0)\) and \((0, 1)\)
9. \(x\)-int: -6 , \(y\)-int: -8
x y 5 10 -5 -10 5 10 -5 -10
Plot \((-6, 0)\) and \((0, -8)\)
Remember: \(x\)-intercepts always lie on the horizontal axis; \(y\)-intercepts lie on the vertical axis.
Page 1 of 2
Algebra 1 • Unit 2 Review
Graphing Standard Form & Special Lines
Student Name: _______________________
Part 3: Find intercepts, then graph each line
Enlarged Grids (-10 to +10)
10. \(-5x + y = -10\)
\(x\)-int: _____
\(y\)-int: _____
x y 5 10 -5 -10 5 10 -5 -10
11. \(-3x - 6y = 12\)
\(x\)-int: _____
\(y\)-int: _____
x y 5 10 -5 -10 5 10 -5 -10
12. \(4x - 12y = -24\)
\(x\)-int: _____
\(y\)-int: _____
x y 5 10 -5 -10 5 10 -5 -10
Special Lines Cheat Sheet: HOY vs VUX
Memory Trick
H • O • Y
• H orizontal • O -Slope (\(m = 0\)) • Y = #
\(y = -2\) Horizontal
V • U • X
• V ertical • U ndefined slope • X = #
\(x = 0\) Vertical
Part 4: Identify Line Type
Tell whether graph is horizontal or vertical:
13. \(y = -2\)
Line Type: _________________
14. \(x = 0\)
Line Type: _________________
*Hint: \(x = 0\) is the equation of the y-axis itself!
Part 5: Graph each equation
Draw and label arrows on both ends of your line:
15. \(y = 6\) x y 5 -5 5 -5
16. \(x = -2\) x y 5 -5 5 -5
Pro Tip: On quizzes, write intercepts as coordinate pairs \((x, 0)\) and \((0, y)\) for full credit!
Page 2 of 2
Standard Form Guide Key Teacher Solutions & Grading Guide
Standard Form & Intercepts Study Guide Key
Teacher Key • Page 1
Standard: CCSS.MATH.CONTENT.HSA.CED.A.2
Unit: Linear Equations & Graphing
Format: Intercepts & Graphs
Teacher Grading Standards for Intercepts
Scoring Tip
Accept either coordinate point format \((x, 0)\) and \((0, y)\) or single variable format \(x = \#\) and \(y = \#\). Strongly encourage ordered pairs to reinforce that intercepts represent points on the coordinate plane.
Part 1 Solutions: x- and y-Intercepts
Items 1–6 (1 pt per intercept)
1. \(x + y = 7\) Let \(y=0\), \(x=0\)
\(x\)-int: \(7\) or \((7, 0)\)
\(y\)-int: \(7\) or \((0, 7)\)
2. \(x - 3y = 9\) \(-3y=9 \implies y=-3\)
\(x\)-int: \(9\) or \((9, 0)\)
\(y\)-int: \(-3\) or \((0, -3)\)
3. \(2x + 3y = -6\) \(2x=-6, 3y=-6\)
\(x\)-int: \(-3\) or \((-3, 0)\)
\(y\)-int: \(-2\) or \((0, -2)\)
4. \(-4x - 2y = -8\) \(-4x=-8, -2y=-8\)
\(x\)-int: \(2\) or \((2, 0)\)
\(y\)-int: \(4\) or \((0, 4)\)
5. \(5x - 4y = -12\) \(5x=-12, -4y=-12\)
\(x\)-int: \(-\frac{12}{5}\) or \((-2.4, 0)\)
\(y\)-int: \(3\) or \((0, 3)\)
6. \(-2x + 7y = 11\) \(-2x=11, 7y=11\)
\(x\)-int: \(-\frac{11}{2}\) or \((-5.5, 0)\)
\(y\)-int: \(\frac{11}{7}\) or \((0, \frac{11}{7})\)
Part 2 Solutions: Plotted Intercepts & Graphs
Items 7–9 (Intervals: -10 to +10)
7. \(x\)-int: 4, \(y\)-int: 5 Slope: -5/4
x y 5 10 -5 -10 5 10 -5 -10 (4,0) (0,5)
Equation: \(5x + 4y = 20\)
8. \(x\)-int: -3, \(y\)-int: 1 Slope: 1/3
x y 5 10 -5 -10 5 10 -5 -10 (-3,0) (0,1)
Equation: \(x - 3y = -3\)
9. \(x\)-int: -6, \(y\)-int: -8 Slope: -4/3
x y 5 10 -5 -10 5 10 -5 -10 ((-6,0) (0,-8)
Equation: \(4x + 3y = -24\)
Standard Form Guide Answer Key Page 1 of 2
Teacher Solutions & Grading Guide
Graphing Standard Form & Special Lines Key
Teacher Key • Page 2
Part 3 Solutions: Intercepts & Complete Graphs
Items 10–12 (Intervals: -10 to +10)
10. \(-5x + y = -10\)
\(x\)-int: \(2\)
\(y\)-int: \(-10\)
x y 5 10 -5 -10 5 10 -5 -10 (2,0) (0,-10)
11. \(-3x - 6y = 12\)
\(x\)-int: \(-4\)
\(y\)-int: \(-2\)
x y 5 10 -5 -10 5 10 -5 -10 (-4,0) (0,-2)
12. \(4x - 12y = -24\)
\(x\)-int: \(-6\)
\(y\)-int: \(2\)
x y 5 10 -5 -10 5 10 -5 -10 (-6,0) (0,2)
Part 4 Solutions: Line Types
Verification using HOY VUX rule:
13. \(y = -2\)
Classification: Horizontal Line
Slope \(m = 0\); crosses y-axis at \(-2\).
14. \(x = 0\)
Classification: Vertical Line
Slope is undefined; equation of y-axis.
Part 5 Solutions: Graphed Lines
Verify horizontal/vertical alignment and arrows:
15. \(y = 6\) (Horizontal) x y 5 -5 5 -5 (0,6)
16. \(x = -2\) (Vertical) x y 5 -5 5 -5 (-2,0)
Common Test Pitfalls to Review Before the Quiz:
• Sign errors with negative coefficients: In \(-4x - 2y = -8\), remind students that dividing \(-8\) by \(-2\) yields positive \(4\).Confusing \(x = \#\) and \(y = \#\): Students frequently draw vertical lines for \(y = \#\). Reiterate: \(y = \#\) must cross the y-axis horizontally!
Standard Form Guide Answer Key Page 2 of 2
Parallel Perpendicular Reteaching Worksheet Algebra 1 • Lesson 5-6 Reteaching
Parallel Lines
Same Slope: \(m_1 = m_2\)
Name:
Class/Period:
Date:
Core Rule & Step-by-Step Model Problem
Parallel Lines Never Intersect
Nonvertical lines are parallel if they have the same slope and different \(y\)-intercepts.Example: \(y = 2x - 6\) and \(y = 2x + 3\) are parallel because both slopes are \(m = 2\).
Problem: Write equation through \((8, 7)\) parallel to \(y = \frac{3}{4}x + 2\) Slope-Intercept Form: \(y = mx + b\)
Step 1: Identify Slope Given slope is \(\frac{3}{4}\). Parallel slope must also be \(m = \mathbf{\frac{3}{4}}\).
Step 2: Point-Slope Form \(y - y_1 = m(x - x_1)\)
Step 3: Solve for y \(y - 7 = \frac{3}{4}x - 6\)\(y = \frac{3}{4}x + 1\)
1. Writing Exercise: Are the graphs of \(y = \frac{2}{3}x + 3\) and \(y = \frac{2}{5}x - 4\) parallel? Explain how you know.
Explanation:
Write an equation in slope-intercept form parallel to the given line
Use point-slope form: \(y - y_1 = m(x - x_1)\)
2. Passes through \((3, 1)\); parallel to \(y = 2x + 4\)
Parallel slope \(m =\) _________ Point \((x_1, y_1) = (3, 1)\)
Point-slope setup: \(y - \) ____ \( = \) ____ \((x - \) ____ \()\)
Final Answer: \(y =\) __________________
3. Passes through \((1, 3)\); parallel to \(y = 7x + 5\)
Parallel slope \(m =\) _________ Point \((x_1, y_1) = (1, 3)\)
Point-slope setup: \(y - \) ____ \( = \) ____ \((x - \) ____ \()\)
Final Answer: \(y =\) __________________
4. Passes through \((1, 6)\); parallel to \(y = 9x - 5\)
Parallel slope \(m =\) _________ Point \((x_1, y_1) = (1, 6)\)
Point-slope setup: \(y - \) ____ \( = \) ____ \((x - \) ____ \()\)
Final Answer: \(y =\) __________________
5. Passes through \((0, 0)\); parallel to \(y = -\frac{1}{2}x - 4\)
Parallel slope \(m =\) _________ Point is the Origin \((0, 0)\)
Point-slope setup: \(y - \) ____ \( = \) ____ \((x - \) ____ \()\)
Final Answer: \(y =\) __________________
6. Passes through \((-5, 7)\); parallel to \(y = -\frac{2}{5}x - 3\)
Parallel slope \(m =\) _________ Watch signs with \(x - (-5)\)!
Point-slope setup: \(y - \) ____ \( = \) ____ \((x + \) ____ \()\)
Final Answer: \(y =\) __________________
7. Passes through \((6, 6)\); parallel to \(y = \frac{1}{3}x - 1\)
Parallel slope \(m =\) _________ Point \((x_1, y_1) = (6, 6)\)
Point-slope setup: \(y - \) ____ \( = \) ____ \((x - \) ____ \()\)
Final Answer: \(y =\) __________________
Key Check: Parallel lines must have identical slopes \(m\) and different \(y\)-intercepts \(b\).
Page 1 of 2
Algebra 1 • Lesson 5-6 Reteaching (Continued)
Perpendicular Lines
Opposite Reciprocals: \(m_1 \cdot m_2 = -1\)
Name:
Date:
Core Rule & Step-by-Step Model Problem
Intersect at Right Angles (90°)
Two lines are perpendicular if the product of their slopes is \(-1\) (they are opposite reciprocals : flip the fraction and change the sign).Example: \(y = -\frac{4}{5}x - 5\) and \(y = \frac{5}{4}x + 4\) are perpendicular because \(-\frac{4}{5} \cdot \frac{5}{4} = -1\).
Problem: Write equation through \((2, 11)\) perpendicular to \(y = \frac{1}{4}x - 5\) Opposite Reciprocal: \(\frac{1}{4} \to -4\)
Step 1: Perpendicular Slope Given slope is \(\frac{1}{4}\). Flip and negate: \(m_\perp = \mathbf{-4}\) because \(\frac{1}{4}(-4) = -1\).
Step 2: Point-Slope Form \(y - y_1 = m(x - x_1)\)
Step 3: Solve for y \(y - 11 = -4x + 8\)\(y = -4x + 19\)
8. Writing Exercise: Are the graphs of \(y = \frac{2}{3}x + 6\) and \(y = -\frac{3}{2}x - 4\) parallel, perpendicular, or neither? Explain how you know.
Explanation:
Write an equation in slope-intercept form perpendicular to the given line
Flip the slope and change the sign first!
9. Passes through \((5, -3)\); \(\perp\) to \(y = 5x + 3\)
Perpendicular slope \(m_\perp =\) _________ Given \(m = 5 \implies m_\perp = -\frac{1}{5}\)
Point-slope setup: \(y - \) ____ \( = \) ____ \((x - \) ____ \()\)
Final Answer: \(y =\) __________________
10. Passes through \((4, 8)\); \(\perp\) to \(y = -2x - 4\)
Perpendicular slope \(m_\perp =\) _________ Given \(m = -2 \implies m_\perp = \frac{1}{2}\)
Point-slope setup: \(y - \) ____ \( = \) ____ \((x - \) ____ \()\)
Final Answer: \(y =\) __________________
11. Passes through \((-2, -5)\); \(\perp\) to \(y = x + 3\)
Perpendicular slope \(m_\perp =\) _________ Given \(m = 1 \implies m_\perp = -1\)
Point-slope setup: \(y - \) ____ \( = \) ____ \((x - \) ____ \()\)
Final Answer: \(y =\) __________________
12. Passes through \((6, 0)\); \(\perp\) to \(y = \frac{3}{2}x - 6\)
Perpendicular slope \(m_\perp =\) _________ Given \(m = \frac{3}{2} \implies m_\perp = -\frac{2}{3}\)
Point-slope setup: \(y - \) ____ \( = \) ____ \((x - \) ____ \()\)
Final Answer: \(y =\) __________________
13. Passes through \((5, 3)\); \(\perp\) to \(y = 5x + 2\)
Perpendicular slope \(m_\perp =\) _________ Given \(m = 5 \implies m_\perp = -\frac{1}{5}\)
Point-slope setup: \(y - \) ____ \( = \) ____ \((x - \) ____ \()\)
Final Answer: \(y =\) __________________
14. Passes through \((7, 1)\); \(\perp\) to \(y = -\frac{7}{2}x + 6\)
Perpendicular slope \(m_\perp =\) _________ Given \(m = -\frac{7}{2} \implies m_\perp = \frac{2}{7}\)
Point-slope setup: \(y - \) ____ \( = \) ____ \((x - \) ____ \()\)
Final Answer: \(y =\) __________________
Key Check: Perpendicular lines have slopes that multiply to \(-1\) (\(m_1 \cdot m_2 = -1\)).
Page 2 of 2
Parallel Perpendicular Reteaching Key Teacher Edition & Solutions
Parallel Lines Reteaching Key
Teacher Key • Page 1
Standard: CCSS.MATH.CONTENT.HSG.GPE.B.5
Topic: Parallel Slopes (\(m_1 = m_2\))
Total: 7 Problems (Page 1)
Parallel Lines Rule & Scoring Guidance
Slope Matching
Parallel lines must have identical slopes (\(m_\parallel = m\)). Award 1 point for correctly identifying the parallel slope and 1 point for accurate point-slope distribution to final slope-intercept form (\(y = mx + b\)).
1. Writing Solution: Are the graphs of \(y = \frac{2}{3}x + 3\) and \(y = \frac{2}{5}x - 4\) parallel?
NO. The slopes are NOT equal (\(m_1 = \frac{2}{3}\) and \(m_2 = \frac{2}{5}\)). Since \(\frac{2}{3} \neq \frac{2}{5}\), the lines are not parallel and will intersect.
Part 1 Solutions: Equations of Parallel Lines
Items 2–7
2. \((3, 1)\); parallel to \(y = 2x + 4\) \(m = 2\)
\(y - 1 = 2(x - 3)\)
\(y - 1 = 2x - 6 \implies y = 2x - 6 + 1\)
Correct Equation: \(y = 2x - 5\)
3. \((1, 3)\); parallel to \(y = 7x + 5\) \(m = 7\)
\(y - 3 = 7(x - 1)\)
\(y - 3 = 7x - 7 \implies y = 7x - 7 + 3\)
Correct Equation: \(y = 7x - 4\)
4. \((1, 6)\); parallel to \(y = 9x - 5\) \(m = 9\)
\(y - 6 = 9(x - 1)\)
\(y - 6 = 9x - 9 \implies y = 9x - 9 + 6\)
Correct Equation: \(y = 9x - 3\)
5. \((0, 0)\); parallel to \(y = -\frac{1}{2}x - 4\) \(m = -\frac{1}{2}\)
\(y - 0 = -\frac{1}{2}(x - 0)\)
\(y = -\frac{1}{2}x + 0 \implies b = 0\) (passes through origin)
Correct Equation: \(y = -\frac{1}{2}x\)
6. \((-5, 7)\); parallel to \(y = -\frac{2}{5}x - 3\) \(m = -\frac{2}{5}\)
\(y - 7 = -\frac{2}{5}(x - (-5)) = -\frac{2}{5}(x + 5)\)
\(y - 7 = -\frac{2}{5}x - 2 \implies y = -\frac{2}{5}x - 2 + 7\)
Correct Equation: \(y = -\frac{2}{5}x + 5\)
7. \((6, 6)\); parallel to \(y = \frac{1}{3}x - 1\) \(m = \frac{1}{3}\)
\(y - 6 = \frac{1}{3}(x - 6)\)
\(y - 6 = \frac{1}{3}x - 2 \implies y = \frac{1}{3}x - 2 + 6\)
Correct Equation: \(y = \frac{1}{3}x + 4\)
Lesson 5-6 Reteaching Answer Key Page 1 of 2
Teacher Edition & Solutions
Perpendicular Lines Reteaching Key
Teacher Key • Page 2
Standard: CCSS.MATH.CONTENT.HSG.GPE.B.5
Topic: Opposite Reciprocals (\(m_1 \cdot m_2 = -1\))
Total: 7 Problems (Page 2)
Perpendicular Slopes Rule & Common Pitfalls
Opposite Reciprocal
Common mistake: Students often forget to both flip the fraction and negate the sign (e.g. flipping \(5\) to \(\frac{1}{5}\) without making it \(-\frac{1}{5}\)). Verify both actions before writing point-slope form.
8. Writing Solution: Are the graphs of \(y = \frac{2}{3}x + 6\) and \(y = -\frac{3}{2}x - 4\) parallel, perpendicular, or neither?
PERPENDICULAR. The slopes \(\frac{2}{3}\) and \(-\frac{3}{2}\) are opposite reciprocals. Multiplying them confirms: \(\frac{2}{3} \cdot \left(-\frac{3}{2}\right) = -\frac{6}{6} = -1\).
Part 2 Solutions: Equations of Perpendicular Lines
Items 9–14
9. \((5, -3)\); \(\perp\) to \(y = 5x + 3\) \(m_\perp = -\frac{1}{5}\)
\(y - (-3) = -\frac{1}{5}(x - 5) \implies y + 3 = -\frac{1}{5}x + 1\)
\(y = -\frac{1}{5}x + 1 - 3\)
Correct Equation: \(y = -\frac{1}{5}x - 2\)
10. \((4, 8)\); \(\perp\) to \(y = -2x - 4\) \(m_\perp = \frac{1}{2}\)
\(y - 8 = \frac{1}{2}(x - 4) = \frac{1}{2}x - 2\)
\(y = \frac{1}{2}x - 2 + 8\)
Correct Equation: \(y = \frac{1}{2}x + 6\)
11. \((-2, -5)\); \(\perp\) to \(y = x + 3\) \(m_\perp = -1\)
\(y - (-5) = -1(x - (-2)) \implies y + 5 = -1(x + 2)\)
\(y + 5 = -x - 2 \implies y = -x - 7\)
Correct Equation: \(y = -x - 7\)
12. \((6, 0)\); \(\perp\) to \(y = \frac{3}{2}x - 6\) \(m_\perp = -\frac{2}{3}\)
\(y - 0 = -\frac{2}{3}(x - 6)\)
\(y = -\frac{2}{3}x + 4\)
Correct Equation: \(y = -\frac{2}{3}x + 4\)
13. \((5, 3)\); \(\perp\) to \(y = 5x + 2\) \(m_\perp = -\frac{1}{5}\)
\(y - 3 = -\frac{1}{5}(x - 5) = -\frac{1}{5}x + 1\)
\(y = -\frac{1}{5}x + 1 + 3\)
Correct Equation: \(y = -\frac{1}{5}x + 4\)
14. \((7, 1)\); \(\perp\) to \(y = -\frac{7}{2}x + 6\) \(m_\perp = \frac{2}{7}\)
\(y - 1 = \frac{2}{7}(x - 7) = \frac{2}{7}x - 2\)
\(y = \frac{2}{7}x - 2 + 1\)
Correct Equation: \(y = \frac{2}{7}x - 1\)
Lesson 5-6 Reteaching Answer Key Page 2 of 2
Linear Word Problems Answer Key Teacher Edition & Full Solutions
Linear Word Problems: Teacher Key
Key • Page 1 of 2
Standard: CCSS.MATH.CONTENT.HSA.CED.A.2
Coverage: Problems 1–5 (Front)
Grading: 2 pts per problem
Grading Standards: Award 1 point for the correct equation and 1 point for accurate algebraic substitution and units. Full Credit Guide
1. 100-point test (2-point & 4-point questions) Total = 100
\(x =\) # of 2-pt questions
\(y =\) # of 4-pt questions
a. Equation: \(2x + 4y = 100\)
b. If \(y = 24\): \(2x + 96 = 100 \implies \mathbf{x = 2}\)
2. Louise's $36 in five-dollar bills and singles Total = $36
\(x =\) # of $5 bills
\(y =\) # of $1 singles
a. Equation: \(5x + y = 36\)
b. If \(x = 2\): \(10 + y = 36 \implies \mathbf{y = 26}\text{ singles}\)
3. Ramy family: 4 sandwiches and 3 salads for $24 Total = $24
\(x =\) cost of sandwich ($)
\(y =\) cost of salad ($)
a. Equation: \(4x + 3y = 24\)
b. If \(x = \$3.75\): \(15 + 3y = 24 \implies \mathbf{y = \$3.00}\)
4. Baby weight: (5 mo, 14 lbs) and (10 mo, 21 lbs) Slope \(m = \frac{7}{5} = 1.4\)
a. Equation: \(y = 1.4x + 7\)
b. Birth Weight (\(x = 0\)): \(7\text{ lbs}\)
c. Monthly Gain: \(1.4\text{ lbs / month}\)
5. Family reunion: $90 on burgers ($1.50 ea.) and turkey burgers ($2.00 ea.) Total = $90
a. Equation: \(1.50x + 2y = 90\)
b. If \(y = 30\): \(1.50x + 60 = 90 \implies \mathbf{x = 20}\text{ burgers}\)
Topic 2 Teacher Solutions Page 1 of 2 (Front Key)
Teacher Edition & Full Solutions
Linear Word Problems: Teacher Key
Key • Page 2 of 2
Standard: CCSS.MATH.CONTENT.HSA.CED.A.2
Coverage: Problems 6–10 (Back)
Grading: 2 pts per problem
6. Carnival drinks: Lemonade ($2/cup) and orange drinks ($3/cup) Total = $240
a. Equation: \(2x + 3y = 240\)
b. If \(x = 60\): \(120 + 3y = 240 \implies \mathbf{y = 40}\text{ drinks}\)
7. Calf weight: (2 mo, 18 lbs) and (8 mo, 36 lbs) Slope \(m = \frac{18}{6} = 3\text{ lbs/mo}\)
a. Equation: \(y = 3x + 12\)
b. Birth Weight: \(12\text{ lbs}\)
c. At 12 Months: \(48\text{ lbs}\)
d. Rate of Gain: \(3\text{ lbs / month}\)
8. Weightlifting: 45-lb plates (\(x\)) and 10-lb plates (\(y\)) to lift 260 lbs Total = 260
a. Equation: \(45x + 10y = 260\)
b. If \(y = 8\): \(45x + 80 = 260 \implies \mathbf{x = 4}\text{ plates}\)
9. Detroit taxi: (2 mi, $11) and (4 mi, $18) Rate \(m = \frac{7}{2} = \$3.50\text{/mi}\)
a. Equation: \(y = 3.5x + 4\)
b. Initial Fee: \$4.00 base
c. Price / Mile: \$3.50 / mile
d. For 10 Miles: \$39.00
10. Backpack coins: $.80 total in dimes (\(x\)) and quarters (\(y\)) Total = $0.80
a. Equation: \(0.10x + 0.25y = 0.80\)
b. If \(y = 2\): \(0.10x + 0.50 = 0.80 \implies \mathbf{x = 3}\text{ dimes}\)
Topic 2 Teacher Solutions Page 2 of 2 (Back Key)
Linear Word Problems Handout Algebra 1 • Topic 2 Practice
Linear Word Problems: Modeling & Applications
Page 1 of 2
Name:
Period:
Date:
Strategy: Use Standard Form (\(Ax + By = C\)) when two rates combine for a fixed total. Use Slope-Intercept (\(y = mx + b\)) when finding rate of change and start value.
1. A 100-point test has \(x\) questions worth 2 points apiece and \(y\) questions worth 4 points apiece.
\(x =\)
\(y =\)
Total:
a. Write an equation describing all questions:
b. If \(y = 24\) four-point questions, find \(x\):
2. Louise has $36 in five-dollar bills and singles. How many of each type of bill does she have?
\(x =\)
\(y =\)
Total:
a. Write an equation:
b. If Louise has 2 five-dollar bills, how many singles?
3. The Ramy family bought 4 sandwiches and 3 salads for $24. Let \(x\) = sandwich cost and \(y\) = salad cost.
\(x =\)
\(y =\)
Total:
a. Write an equation:
b. If each sandwich costs $3.75, find cost of a salad:
4. A baby weighs 14 pounds at 5 months and 21 pounds at 10 months. Let \(x\) = age and \(y\) = weight.
a. Equation in \(y = mx + b\) form:
b. Weight at birth (\(x = 0\)):
c. Monthly weight gain:
5. Family reunion: You spend $90 on hamburgers ($1.50 ea.) and turkey burgers ($2.00 ea.). Let \(x\) = hamburgers and \(y\) = turkey burgers.
a. Write equation in standard form:
b. If you buy 30 turkey burgers, how many hamburgers?
Topic 2 Word Problems Handout Page 1 of 2 (Front)
Algebra 1 • Topic 2 Practice Continued
Linear Word Problems: Modeling & Applications
Page 2 of 2
Student Name:
Period:
6. Carnival drinks: Lemonade sells for $2/cup and orange drinks for $3/cup. Sales totaled $240. Let \(x\) = lemonade and \(y\) = orange drinks.
a. Write equation in standard form:
b. If you sold 60 cups of lemonade, how many orange drinks?
7. A calf weighs 18 lbs. at 2 months old and 36 lbs. at 8 months old. Let \(x\) = age (months) and \(y\) = weight (lbs).
a. Equation in slope-intercept form (\(y = mx + b\)):
b. Calf's weight at birth:
c. Approximate weight at 12 months:
d. Weight gained each month:
8. Weightlifting: A lifter uses 45-lb plates (\(x\)) and 10-lb plates (\(y\)) to lift 260 pounds total.
a. Write equation in standard form:
b. If he uses eight 10-lb plates, how many 45-lb plates?
9. Detroit taxi ride costs $11 for 2 miles and $18 for 4 miles. Let \(x\) = miles and \(y\) = total fare ($).
a. Equation in slope-intercept form:
b. Initial fee (base charge):
c. Price per mile (slope):
d. Cost for a 10-mile ride:
10. Backpack coins: You have $.80 in dimes (\(x\)) and quarters (\(y\)).
a. Write equation in standard form:
b. If you have 2 quarters, how many dimes do you have?
Topic 2 Word Problems Handout Page 2 of 2 (Back)
Rotating Shapes Worksheet Geometry • Rigid Transformations
Rotating Shapes on the Coordinate Plane
Page 1 of 2
Name:
Period:
Date:
Coordinate Rules for Rotations About Origin (0,0)
CCW = Counterclockwise • CW = Clockwise
90° CW (270° CCW) \((x, y) \to (y, -x)\)
180° Rotation (Any) \((x, y) \to (-x, -y)\)
90° CCW (270° CW) \((x, y) \to (-y, x)\)
Record new coordinates in the boxes below each graph, then plot and connect!
1. Rotation: 180° about origin \((-x, -y)\)
x y 5 -5 5 -5
(1, 2) → ( , )
(2, 4) → ( , )
(3, 1) → ( , )
2. Rotation: 90° CW about origin \((y, -x)\)
x y 5 -5 5 -5
(1, 0) → ( , )
(4, -4) → ( , )
(1, -2) → ( , )
3. Rotation: 90° CCW about origin \((-y, x)\)
x y 5 -5 5 -5
(-3, -2) → ( , )
(0, -1) → ( , )
(-1, -4) → ( , )
4. Rotation: 90° CCW about origin \((-y, x)\)
x y 5 -5 5 -5
(-3, 3) → ( , )
(-1, 2) → ( , )
(-2, 1) → ( , )
Rotating Shapes on the Coordinate Plane Page 1 of 2
Geometry Transformations • Practice Continued
Rotating Shapes on the Coordinate Plane
Page 2 of 2
Student Name:
Period:
5. Rotation: 180° about origin \((-x, -y)\)
x y 5 -5 5 -5
(-4, -3) → ( , )
(0, -1) → ( , )
(-2, -4) → ( , )
6. Rotation: 90° CW about origin \((y, -x)\)
x y 5 -5 5 -5
(1, 1) → ( , )
(3, 4) → ( , )
(4, 1) → ( , )
7. Rotation: 270° CCW (90° CW) \((y, -x)\)
x y 5 -5 5 -5
(-4, 1) → ( , )
(-1, 4) → ( , )
(-1, 1) → ( , )
8. Rotation: 180° about origin \((-x, -y)\)
x y 5 -5 5 -5
(1, 1) → ( , )
(4, 1) → ( , )
(4, 3) → ( , )
(1, 3) → ( , )
Algebraic Coordinate Predictions (Without Graphing)
9. Point \(A(-5, 2)\) is rotated 90° CCW about the origin.
Image: \(A'\) ( , )
10. \(\triangle JKL\) with vertices \(J(3, -4), K(1, -1), L(5, 2)\) is rotated 180° .
\(J'\) ( , ) \(K'\) ( , ) \(L'\) ( , )
Rotating Shapes on the Coordinate Plane Page 2 of 2
Rotating Shapes Key Teacher Edition & Full Solutions
Rotating Shapes Answer Key
Key • Page 1 of 2
Standard: CCSS.MATH.CONTENT.8.G.A.3
Visual Key: Green = Pre-Image • Red = Rotated Image
Center: Origin (0,0)
90° CW / 270° CCW \((x, y) \to (y, -x)\)
180° Rotation (Any) \((x, y) \to (-x, -y)\)
90° CCW / 270° CW \((x, y) \to (-y, x)\)
1. Rotation: 180° about origin \((-x, -y)\)
(1, 2) → (-1, -2)
(2, 4) → (-2, -4)
(3, 1) → (-3, -1)
2. Rotation: 90° CW about origin \((y, -x)\)
(1, 0) → (0, -1)
(4, -4) → (-4, -4)
(1, -2) → (-2, -1)
3. Rotation: 90° CCW about origin \((-y, x)\)
(-3, -2) → (2, -3)
(0, -1) → (1, 0)
(-1, -4) → (4, -1)
4. Rotation: 90° CCW about origin \((-y, x)\)
(-3, 3) → (-3, -3)
(-1, 2) → (-2, -1)
(-2, 1) → (-1, -2)
Geometry Answer Key Page 1 of 2
Teacher Edition & Full Solutions
Rotating Shapes Answer Key
Key • Page 2 of 2
Coverage: Problems 5–10 (Extended Practice)
Visual Key: Green = Pre-Image • Red = Image
Grading: Full Credit Verified
5. Rotation: 180° about origin \((-x, -y)\)
(-4, -3) → (4, 3)
(0, -1) → (0, 1)
(-2, -4) → (2, 4)
6. Rotation: 90° CW about origin \((y, -x)\)
(1, 1) → (1, -1)
(3, 4) → (4, -3)
(4, 1) → (1, -4)
7. Rotation: 270° CCW (90° CW) \((y, -x)\)
(-4, 1) → (1, 4)
(-1, 4) → (4, 1)
(-1, 1) → (1, 1)
8. Rotation: 180° about origin \((-x, -y)\)
(1, 1) → (-1, -1)
(4, 1) → (-4, -1)
(4, 3) → (-4, -3)
(1, 3) → (-1, -3)
Algebraic Coordinate Prediction Solutions
9. \(A(-5, 2)\) rotated 90° CCW about origin \(\to (-y, x)\):
Image: \(A'(-2, -5)\)
10. \(\triangle JKL\) rotated 180° about origin \(\to (-x, -y)\):
\(J'(-3, 4)\) \(K'(-1, 1)\) \(L'(-5, -2)\)
Geometry Answer Key Page 2 of 2
Rotation Showdown Game Activity Collaborative Learning • Partner Battle
Rotation Showdown: Connect & Capture
2-Player Review Game
Player 1 (O):
Player 2 (X):
Period:
How to Play
Goal: 4 in a row OR most captured tiles!
1. Players take turns picking an unclaimed tile. Both players record their work on Page 2.2. If the active player gets it correct, they claim the tile with their symbol (O or X). If wrong, the opponent can steal!3. Check answers using the Referee Key on Page 2. First to connect 4 tiles in a row (horizontally, vertically, or diagonally) or control the most tiles wins!
TILE #1
Rotate point (3, -5) by 90° CCW .
Image: (____, ____)
TILE #2
Rotate point (-4, 7) by 180° .
Image: (____, ____)
TILE #3
Rotate point (2, 6) by 90° CW .
Image: (____, ____)
TILE #4
Which single rotation turns Quad I into Quad IV ?
Angle: _________
TILE #5
Rotate point (-8, -1) by 180° .
Image: (____, ____)
TILE #6
Rotate point (-3, 0) by 90° CW .
Image: (____, ____)
TILE #7
Rotate point (0, 5) by 90° CCW .
Image: (____, ____)
TILE #8
A 270° CCW rotation is identical to what CW rotation?
CW Angle: _______
TILE #9
Rotate point (6, -4) by 180° .
Image: (____, ____)
TILE #10
Rotate point (-2, -9) by 90° CW .
Image: (____, ____)
TILE #11
Rotate point (7, 1) by 270° CCW .
Image: (____, ____)
TILE #12
Reverse: After 180°, image is (5, -3) . Original point?
Pre-image: (____, ____)
TILE #13
Rotate point (-4, -4) by 90° CCW .
Image: (____, ____)
TILE #14
Rotate point (10, -2) by 360° .
Image: (____, ____)
TILE #15
Reverse: After 90° CW, image is (1, -4) . Original point?
Pre-image: (____, ____)
TILE #16
True or False: Rotating by 180° always negates both coordinates.
Circle: TRUE / FALSE
Rotation Showdown Activity Page 1 of 2 (Game Board)
Match Workspaces & Verification
Showdown Worksheets & Referee Verification Key
Page 2 of 2
Player 1 Workspace (Symbol: O) Tiles Claimed: _____
Record tile # and show your coordinate rule work:
Tile #___:
Answer: (___, ___)
Tile #___:
Answer: (___, ___)
Tile #___:
Answer: (___, ___)
Tile #___:
Answer: (___, ___)
Tile #___:
Answer: (___, ___)
Player 1 Score: ________
Player 2 Workspace (Symbol: X) Tiles Claimed: _____
Record tile # and show your coordinate rule work:
Tile #___:
Answer: (___, ___)
Tile #___:
Answer: (___, ___)
Tile #___:
Answer: (___, ___)
Tile #___:
Answer: (___, ___)
Tile #___:
Answer: (___, ___)
Player 2 Score: ________
Official Referee Verification Key (Check after both players agree)
Fold or cover during match
#1: (5, 3)
#2: (4, -7)
#3: (6, -2)
#4: 90° CW (270° CCW)
#5: (8, 1)
#6: (0, 3)
#7: (-5, 0)
#8: 90° CW
#9: (-6, 4)
#10: (-9, 2)
#11: (1, -7)
#12: (-5, 3)
#13: (4, -4)
#14: (10, -2)
#15: (4, 1)
#16: TRUE
Winner: ____________________________________
Page 2 of 2 (Referee & Workspaces)
