Plane Shift Worksheet Grade 8 Math Transformations
Plane Shift Worksheet
Mastering Translations & Coordinate Notation on the Coordinate Plane
Name:
Date:
Period:
Translation Quick Rules
Horizontal Shift (\(x\))
• Right: Add to \(x\) \(\rightarrow (x + a)\)Left: Subtract from \(x\) \(\rightarrow (x - a)\)
Vertical Shift (\(y\))
• Up: Add to \(y\) \(\rightarrow (y + b)\)Down: Subtract from \(y\) \(\rightarrow (y - b)\)
Mapping Rule
Pre-Image \(\to\) Image
1 Warm-Up: Translating Single Points
Fill in each blank to complete the table
Original Point Translation Words Coordinate Rule New Point (Image) \(A(3, 4)\) Right 2 units, Down 5 units \((x+2, y-5)\) \(A'(5, -1)\) (model) \(B(-2, 5)\) Right 4 units, Up 1 unit \((x + \_\_, y + \_\_)\) \(B'(\_\_\_\_, \_\_\_\_)\) \(C(1, -3)\) Left 3 units, Down 2 units \((x - \_\_, y - \_\_)\) \(C'(\_\_\_\_, \_\_\_\_)\) \(D(-4, -1)\) Right 6 units, Down 3 units \((x \_\_\_\_, y \_\_\_\_)\) \(D'(\_\_\_\_, \_\_\_\_)\)
2 Shape Shift: Translating Triangle \(JKL\)
Rule: 5 units right & 3 units down
x y 2 4 -2 -4 2 4 -2 -4 J K L Plot and label the new image \(J'K'L'\) on the grid!
Step 1: Write the Coordinate Rule
Translate 5 units right and 3 units down:
\((x, y) \to (x\) + 5, \(y\) - 3\()\)
Step 2: Compute New Coordinates
Pre-Image Work \((x+5, y-3)\) Image Point \(J(-4, 1)\) \((-4+5, 1-3)\) \(J'(1, -2)\) \(K(-1, 5)\) \((-1+5, \quad\_\_)\) \(K'(\_\_\_, \_\_\_)\) \(L(-1, 1)\) \((\_\_\_\_\_, \quad\_\_)\) \(L'(\_\_\_, \_\_\_)\)
Check Your Graph:
Did the size or shape of \(\triangle JKL\) change, or did it just slide? Translations preserve both size and shape (they are congruent ).
Plane Shift Worksheet • Grade 8 Mathematics Page 1 of 2
Independent Practice & Mission Challenges
Apply rules, determine unknown shifts, and spot mathematical errors
Page 2
3 Translate Quadrilateral \(PQRS\)
Rule: Translate 4 units left and 3 units up
x y 2 4 -2 -4 2 4 -2 -4 P Q R S Graph and connect \(P'Q'R'S'\) above
Coordinate Rule:
\((x, y) \to (x\) _________, \(y\) _________\()\)
Pre-Image Image Point \(P(1, -1)\) \(P'(\_\_\_\_, \_\_\_\_)\) \(Q(4, -1)\) \(Q'(\_\_\_\_, \_\_\_\_)\) \(R(5, -4)\) \(R'(\_\_\_\_, \_\_\_\_)\) \(S(1, -4)\) \(S'(\_\_\_\_, \_\_\_\_)\)
4 Translation Detectives: What Was the Rule?
Work backwards to find the shift
Case A: Point Mapping
A point \(M(-3, 2)\) is translated to \(M'(4, -1)\).
Horizontal shift: _____ units (Left / Right)
Vertical shift: _____ units (Up / Down)
Rule: \((x, y) \to (x\) _____, \(y\) _____\()\)
T T'
Case B: Graph Vector
Look at the shift from point \(T(-2, 2)\) to \(T'(3, -3)\).
Rule: \((x, y) \to (x\) _____, \(y\) _____\()\)
5 Error Detective: What Went Wrong?
Spot the Mistake
Scenario: Alex was given the point \(W(3, -4)\) and the translation rule: "Translate 2 units left and 5 units up."
A) Explain Alex's mistake in words:
B) Write the correct rule and image \(W'\):
Correct Rule: \((x, y) \to (x\) _____, \(y\) _____\()\)
Correct \(W'\): \(W'(\) _______ , _______ \()\)
Plane Shift Worksheet • Grade 8 Mathematics Page 2 of 2
Plane Shift Answer Key Teacher Guide • Answer Key Grade 8 Geometry
Plane Shift Answer Key
Fully Worked Solutions, Coordinate Mappings & Common Misconceptions
COMPLETE SOLUTIONS
Translations • 8.G.A.1, 8.G.A.3
Teacher Coaching Note
Core Standard: 8.G.A.3
Remind students that translations are rigid transformations (isometries). The pre-image and image are always congruent . The orientation and angles never change—only the position slides across the plane.
1 Section 1: Warm-Up Solutions
Correct answers in bold red
Original Point Translation Words Coordinate Rule New Point (Image) \(A(3, 4)\) Right 2 units, Down 5 units \((x+2, y-5)\) \(A'(5, -1)\) (given) \(B(-2, 5)\) Right 4 units, Up 1 unit \((x + 4, y + 1)\) \(B'(2, 6)\) \(C(1, -3)\) Left 3 units, Down 2 units \((x - 3, y - 2)\) \(C'(-2, -5)\) \(D(-4, -1)\) Right 6 units, Down 3 units \((x + 6, y - 3)\) \(D'(2, -4)\)
2 Section 2: Translating Triangle \(JKL\) Solution
Rule: \((x, y) \to (x + 5, y - 3)\)
x y 2 4 -2 -4 2 4 -2 -4 J K L J'(1,-2) K'(4,2) L'(4,-2) Image \(\triangle J'K'L'\) shown in green above
Step 1: Coordinate Rule
\((x, y) \to (x + 5, y - 3)\)
Step 2: Compute Coordinates
Pre-Image Work Image Point \(J(-4, 1)\) \((-4+5, 1-3)\) \(J'(1, -2)\) \(K(-1, 5)\) \((-1+5, 5-3)\) \(K'(4, 2)\) \(L(-1, 1)\) \((-1+5, 1-3)\) \(L'(4, -2)\)
Common Misconception Alert:
Students often confuse the signs when translating negative coordinates (e.g. calculating \(-4 + 5\) as \(-9\) or \(-1\)). Encourage them to count grid lines as a check!
Plane Shift Answer Key • Grade 8 Mathematics Page 1 of 2
Independent Practice & Mission Solutions
Page 2 Answer Key, Work & Error Analysis Solutions
Page 2 Key
3 Section 3: Quadrilateral \(PQRS\) Solutions
Plane Shift Exit Ticket Exit Ticket
Plane Shift: Quick Check
Name:
Date:
Score: / 4
1. Point \(A(-4, 3)\) is translated 5 units right and 6 units down .
Coordinate Rule:
\((x, y) \to (x\) ___, \(y\) ___\()\)
New Point \(A'\):
\(A'(\) _____ , _____ \()\)
2. Point \(B(2, -5)\) translates to \(B'(-3, -1)\). Describe the translation:
Horizontal shift: _____ units (Left / Right)
Vertical shift: _____ units (Up / Down)
3. Translate point \(P(1, 1)\) by the rule: \((x, y) \to (x - 4, y + 2)\)
P(1,1)
Plot & State \(P'\): \(P'(\) ____, ____\()\)
How confident do you feel about translations?
⭕ Need help ⭕ Getting there ⭕ I've got this!
Cut along dashed line (2 copies per sheet)
Exit Ticket
Plane Shift: Quick Check
Name:
Date:
Score: / 4
1. Point \(A(-4, 3)\) is translated 5 units right and 6 units down .
Coordinate Rule:
\((x, y) \to (x\) ___, \(y\) ___\()\)
New Point \(A'\):
\(A'(\) _____ , _____ \()\)
2. Point \(B(2, -5)\) translates to \(B'(-3, -1)\). Describe the translation:
Horizontal shift: _____ units (Left / Right)
Vertical shift: _____ units (Up / Down)
3. Translate point \(P(1, 1)\) by the rule: \((x, y) \to (x - 4, y + 2)\)
P(1,1)
Plot & State \(P'\): \(P'(\) ____, ____\()\)
How confident do you feel about translations?
⭕ Need help ⭕ Getting there ⭕ I've got this!
Plane Shift Warm Up Bell Ringer
Plane Shift: Warm-Up Launch
Name:
Date:
1 Locate the Radar Blips
Write the coordinates \((x, y)\) for each point:
A B C
\(A(\) ____, ____ \()\)
\(B(\) ____, ____ \()\)
\(C(\) ____, ____ \()\)
Remember: \((x\) comes first, then \(y)\)!
2 Axis Shift Math
Solve each coordinate jump:
\(-3 + 5 =\)
\(4 - 7 =\)
\(-1 - 4 =\)
\(0 + 6 =\)
3 Which One is a Translation?
A translation is a slide without turning or flipping. Circle one:
A Flipped over
B Slid right
C Turned 90°
How confident do you feel starting today's mission?
Need Review
Ready to Slide!
Cut along dashed line (2 copies per sheet)
Bell Ringer
Plane Shift: Warm-Up Launch
Name:
Date:
1 Locate the Radar Blips
Write the coordinates \((x, y)\) for each point:
A B C
\(A(\) ____, ____ \()\)
\(B(\) ____, ____ \()\)
\(C(\) ____, ____ \()\)
Remember: \((x\) comes first, then \(y)\)!
2 Axis Shift Math
Solve each coordinate jump:
\(-3 + 5 =\)
\(4 - 7 =\)
\(-1 - 4 =\)
\(0 + 6 =\)
3 Which One is a Translation?
A translation is a slide without turning or flipping. Circle one:
A Flipped over
B Slid right
C Turned 90°
How confident do you feel starting today's mission?
Need Review
Ready to Slide!
