Transformation Mystery Station Slides 1
GALLERY WALK • STATION 1
RIGID TRANSFORMATION MYSTERY
Blue = Pre-Image Green = Image
x y A B C A′ B′ C′
Coordinate Clues
Pre: A(−3, 1)
Img: A′(3, 1)
Pre: B(−1, 4)
Img: B′(1, 4)
Pre: C(−1, 1)
Img: C′(1, 1)
On Your Recording Sheet:
Check: Reflection, Translation, or Rotation?
Identify: Name specific line, vector shift, or angle.
Write Rule: Coordinate notation (x, y) → ______
Math Station Card • Print & Mount CCSS 8.G.A.3
2
GALLERY WALK • STATION 2
RIGID TRANSFORMATION MYSTERY
Blue = Pre-Image Green = Image
x y D E F G D′ E′ F′ G′
Coordinate Clues
Pre: D(−4, 1)
Img: D′(−4, −1)
Pre: E(−1, 1)
Img: E′(−1, −1)
Pre: F(−2, 4)
Img: F′(−2, −4)
Pre: G(−4, 3)
Img: G′(−4, −3)
On Your Recording Sheet:
Check: Reflection, Translation, or Rotation?
Identify: Name specific line, vector shift, or angle.
Write Rule: Coordinate notation (x, y) → ______
Math Station Card • Print & Mount CCSS 8.G.A.3
3
GALLERY WALK • STATION 3
RIGID TRANSFORMATION MYSTERY
Blue = Pre-Image Green = Image
x = 1 J K L J′ K′ L′
Coordinate Clues
Pre: J(2, 1)
Img: J′(0, 1)
Pre: K(4, 1)
Img: K′(−2, 1)
Pre: L(2, 4)
Img: L′(0, 4)
On Your Recording Sheet:
Transformation Type: State the exact type of movement.
Line Equation: What is the exact equation of reflection?
Verify Distance: Check distance from J and J′ to red line.
Math Station Card • Print & Mount CCSS 8.G.A.3
4
GALLERY WALK • STATION 4
RIGID TRANSFORMATION MYSTERY
Blue = Pre-Image Green = Image
y = −1 P Q R P′ Q′ R′
Coordinate Clues
Pre: P(1, 1)
Img: P′(1, −3)
Pre: Q(4, 1)
Img: Q′(4, −3)
Pre: R(1, 3)
Img: R′(1, −5)
On Your Recording Sheet:
Transformation Type: State the exact type of movement.
Line Equation: What is the exact line of reflection?
Analysis: Why doesn't simple rule (x, −y) work?
Math Station Card • Print & Mount CCSS 8.G.A.3
5
GALLERY WALK • STATION 5
RIGID TRANSFORMATION MYSTERY
Blue = Pre-Image Green = Image
R S T U R′ S′ T′ U′
Coordinate Clues
Pre: R(1, 1)
Img: R′(−1, 1)
Pre: S(4, 1)
Img: S′(−4, 1)
Pre: T(3, 3)
Img: T′(−3, 3)
Pre: U(1, 3)
Img: U′(−1, 3)
On Your Recording Sheet:
Transformation Type: State the exact type of movement.
Description: Describe the flip across vertical axis.
Write Rule: Coordinate notation (x, y) → ______
Math Station Card • Print & Mount CCSS 8.G.A.3
6
GALLERY WALK • STATION 6
RIGID TRANSFORMATION MYSTERY
Blue = Pre-Image Green = Image
A B C A′ B′ C′
Coordinate Clues
Pre: A(−3, −3)
Img: A′(2, −1)
Pre: B(−1, −3)
Img: B′(4, −1)
Pre: C(−3, −1)
Img: C′(2, 1)
On Your Recording Sheet:
Transformation Type: Is it a slide, flip, or turn?
Shift Amounts: Units right/left and units up/down?
Algebraic Rule: Fill in (x, y) → (x ___, y ___)
Math Station Card • Print & Mount CCSS 8.G.A.3
7
GALLERY WALK • STATION 7
RIGID TRANSFORMATION MYSTERY
Blue = Pre-Image Green = Image
D E F D′ E′ F′
Coordinate Clues
Pre: D(1, 4)
Img: D′(−3, 1)
Pre: E(4, 4)
Img: E′(0, 1)
Pre: F(1, 1)
Img: F′(−3, −2)
On Your Recording Sheet:
Transformation Type: State the exact type of movement.
Shift Values: Horizontal and vertical shift amounts.
Write Rule: Coordinate notation (x, y) → ______
Math Station Card • Print & Mount CCSS 8.G.A.3
8
GALLERY WALK • STATION 8
RIGID TRANSFORMATION MYSTERY
Blue = Pre-Image Green = Image
Coordinate Clues
Pre: (−4, 2)
Img: (−1, −2)
Pre: (−1, 2)
Img: (2, −2)
Pre: (−2, 4)
Img: (1, 0)
Pre: (−4, 4)
Img: (−1, 0)
On Your Recording Sheet:
Transformation Type: State the exact type of movement.
Vector Words: Describe slide using direction & shift units.
Check Rule: Verify (x, y) → (x + 3, y − 4)
Math Station Card • Print & Mount CCSS 8.G.A.3
9
GALLERY WALK • STATION 9
RIGID TRANSFORMATION MYSTERY
Blue = Pre-Image Green = Image
Coordinate Clues
Pre: (1, −4)
Img: (−4, −3)
Pre: (4, −4)
Img: (−1, −3)
Pre: (2, −1)
Img: (−3, 0)
On Your Recording Sheet:
Transformation Type: State the exact type of movement.
Shift Analysis: Direction and vector shift amounts.
Confirm Rule: Verify (x, y) → (x − 5, y + 1)
Math Station Card • Print & Mount CCSS 8.G.A.3
10
GALLERY WALK • STATION 10
RIGID TRANSFORMATION MYSTERY
Blue = Pre-Image Green = Image
Coordinate Clues
Pre: (2, 1)
Img: (−4, 1)
Pre: (5, 1)
Img: (−1, 1)
Pre: (2, 4)
Img: (−4, 4)
On Your Recording Sheet:
Transformation Type: State the exact type of movement.
Observation: Notice y stayed identical! What happened to x?
Write Rule: Coordinate notation (x, y) → (x − 6, y)
Math Station Card • Print & Mount CCSS 8.G.A.3
11
GALLERY WALK • STATION 11
RIGID TRANSFORMATION MYSTERY
Blue = Pre-Image Green = Image
Coordinate Clues
Pre: (1, 2)
Img: (2, −1)
Pre: (4, 2)
Img: (2, −4)
Pre: (1, 5)
Img: (5, −1)
On Your Recording Sheet:
Transformation Type: Rotation around center (0, 0)?
Turn Details: 90° Clockwise or Counter-Clockwise?
Algebraic Rule: Verify rule (x, y) → (y, −x)
Math Station Card • Print & Mount CCSS 8.G.A.3
12
GALLERY WALK • STATION 12
RIGID TRANSFORMATION MYSTERY
Blue = Pre-Image Green = Image
Coordinate Clues
Pre: (−4, 1)
Img: (4, −1)
Pre: (−1, 1)
Img: (1, −1)
Pre: (−1, 4)
Img: (1, −4)
On Your Recording Sheet:
Transformation Type: State the exact type of movement.
Sign Pattern: Both x and y flipped signs! What rotation is this?
Algebraic Rule: Verify rule (x, y) → (−x, −y)
Math Station Card • Print & Mount CCSS 8.G.A.3
13
GALLERY WALK • STATION 13
RIGID TRANSFORMATION MYSTERY
Blue = Pre-Image Green = Image
Coordinate Clues
Pre: (2, 1)
Img: (−1, 2)
Pre: (5, 1)
Img: (−1, 5)
Pre: (2, 3)
Img: (−3, 2)
On Your Recording Sheet:
Transformation Type: State the exact type of movement.
Direction & Angle: Degrees and CCW direction?
Algebraic Rule: Verify rule (x, y) → (−y, x)
Math Station Card • Print & Mount CCSS 8.G.A.3
14
GALLERY WALK • STATION 14
RIGID TRANSFORMATION MYSTERY
Blue = Pre-Image Green = Image
Coordinate Clues
Pre: (1, 1)
Img: (−1, −1)
Pre: (4, 1)
Img: (−4, −1)
Pre: (3, 3)
Img: (−3, −3)
Pre: (1, 3)
Img: (−1, −3)
On Your Recording Sheet:
Transformation Type: State the exact type of movement.
Center & Degrees: Center of rotation and degrees?
Algebraic Rule: Verify rule (x, y) → (−x, −y)
Math Station Card • Print & Mount CCSS 8.G.A.3
15
GALLERY WALK • STATION 15
RIGID TRANSFORMATION MYSTERY
Blue = Pre-Image Green = Image
Coordinate Clues
Pre: (−3, 2)
Img: (2, 3)
Pre: (−1, 2)
Img: (2, 1)
Pre: (−1, 4)
Img: (4, 1)
On Your Recording Sheet:
Transformation Type: State the exact type of movement.
Rotation Details: Confirm clockwise turn around origin.
Algebraic Rule: Verify rule (x, y) → (y, −x)
Math Station Card • Print & Mount CCSS 8.G.A.3
★
STATION 16 • BONUS MISSION
COMPOSITE TRANSFORMATION CHALLENGE
Expert Station
x y Start Finish
Two Transformations Occurred!
Start: (1, 1), (3, 1), (1, 4)
Finish: (−3, −1), (−1, −1), (−3, −4)
Bonus Question:
Can you name both steps that took the Blue triangle to the Purple triangle?
💡 Hint: A reflection followed by a translation!
Math Station Card • Print & Mount CCSS 8.G.A.3 Extension
Transformation Mystery Recording Sheet 8th Grade Geometry • CCSS 8.G.A.3
TRANSFORMATION MYSTERY
Gallery Walk Student Recording Sheet • Stations 1–8
Name:
Date:
Period:
Directions: Visit each station card. Determine the transformation from Blue (Pre-Image) to Green (Image), name the key features, and write the algebraic rule.
STATION 1 Mystery Motion
1. Type:
Reflection Translation Rotation
2. Specific line, vector, or angle:
3. Algebraic Rule: (x, y) → ( ________ , ________ )
STATION 2 Mystery Motion
1. Type:
Reflection Translation Rotation
2. Specific line, vector, or angle:
3. Algebraic Rule: (x, y) → ( ________ , ________ )
STATION 3 Line of Reflection
1. Transformation Type:
2. Exact equation of line of reflection:
3. Perpendicular distance from J & J′ to line:
STATION 4 Line of Reflection
1. Transformation Type:
2. Exact line of reflection:
3. Why doesn't rule (x, −y) work here?
STATION 5 Vertical Flip
1. Transformation Type:
2. Describe flip across vertical axis:
3. Algebraic Rule: (x, y) → ( ________ , ________ )
STATION 6 Vector Slide
1. Slide, flip, or turn?
2. Units Right/Left & Up/Down:
3. Algebraic Rule: (x, y) → (x ____ , y ____)
STATION 7 Shift Amounts
1. Transformation Type:
2. Horizontal & Vertical Shift:
3. Coordinate Rule: (x, y) → ( ________ , ________ )
STATION 8 Vector Description
1. Transformation Type:
2. Describe slide using vector words:
3. Verify Rule: (x, y) → (x + 3, y − 4) checks?
Transformations Gallery Walk • Student Recording Sheet Page 1 of 2
8th Grade Geometry • CCSS 8.G.A.3
TRANSFORMATION MYSTERY
Gallery Walk Student Recording Sheet • Stations 9–16
Student Name:
STATION 9 Direction & Shift
1. Transformation Type:
2. Direction and vector shift:
3. Algebraic Rule: (x, y) → ( ________ , ________ )
STATION 10 Single Axis Shift
1. Transformation Type:
2. y stayed identical! What happened to x?
3. Algebraic Rule: (x, y) → ( ________ , ________ )
STATION 11 Rotation Angle
1. Center of Rotation:
2. Degrees & Direction (CW or CCW?):
3. Algebraic Rule: (x, y) → ( ________ , ________ )
STATION 12 Sign Flip Clue
1. Transformation Type:
2. Both x and y flipped signs! Which rotation?
3. Algebraic Rule: (x, y) → ( ________ , ________ )
STATION 13 Counter-Clockwise
1. Transformation Type:
2. Degrees & CCW Direction:
3. Algebraic Rule: (x, y) → ( ________ , ________ )
STATION 14 Origin Rotation
1. Transformation Type:
2. Center of rotation & degrees:
3. Algebraic Rule: (x, y) → ( ________ , ________ )
STATION 15 Clockwise Turn
1. Transformation Type:
2. Confirm turn direction around (0,0):
3. Algebraic Rule: (x, y) → ( ________ , ________ )
★ STATION 16 Bonus Mission
Expert
Step 1 Transformation & Line/Vector:
Step 2 Transformation & Line/Vector:
Combined algebraic description:
Self-Check: Reflections Translations Rotations Composite (Bonus)
Page 2 of 2
Transformation Mystery Answer Key TEACHER REFERENCE • ANSWER KEY
TRANSFORMATION MYSTERY KEY
Stations 1–8 Solutions, Algebraic Rules & Teaching Notes
Standard: CCSS.MATH.CONTENT.8.G.A.3
Total Stations: 16 + Bonus
Scoring Guide: Award 1 pt for Transformation Type, 1 pt for Line/Vector/Angle description, and 1 pt for Algebraic Coordinate Rule (3 pts per station).
STATION 1 Reflection across y-axis
3 pts
1. Type: ☑ Reflection ☐ Translation ☐ Rotation
2. Specific line: y-axis (line x = 0)
3. Algebraic Rule: (x, y) → (−x, y)
💡 Note: x-values change signs while y-values stay identical.
STATION 2 Reflection across x-axis
3 pts
1. Type: ☑ Reflection ☐ Translation ☐ Rotation
2. Specific line: x-axis (line y = 0)
3. Algebraic Rule: (x, y) → (x, −y)
💡 Note: y-values invert signs; figure flips vertically over horizontal axis.
STATION 3 Vertical Mirror Line x = 1
3 pts
1. Type: Reflection
2. Equation of line: x = 1 (vertical line)
3. Distance to line: 1 unit each (perpendicular)
💡 Teaching Tip: J(2,1) is 1 right of x=1; J′(0,1) is 1 left of x=1.
STATION 4 Horizontal Mirror Line y = −1
3 pts
1. Type: Reflection
2. Line of reflection: y = −1 (horizontal line)
3. Why (x, −y) fails: Mirror is y = −1, not y = 0
💡 Common Error: Students confuse reflection over x-axis vs line y = −1.
STATION 5 Reflection across y-axis
3 pts
1. Type: Reflection
2. Flip description: Horizontal flip over y-axis (x = 0)
3. Algebraic Rule: (x, y) → (−x, y)
💡 Note: Quadrilateral points negate x-coordinates: (1,1)→(−1,1).
STATION 6 Translation (+5, +2)
3 pts
1. Motion Type: Slide (Translation)
2. Shift Units: 5 units Right, 2 units Up
3. Algebraic Rule: (x, y) → (x + 5, y + 2)
💡 Verification: A(−3,−3): −3+5 = 2, −3+2 = −1 → A′(2,−1).
STATION 7 Translation (−4, −3)
3 pts
1. Type: Translation
2. Shift amounts: 4 units Left, 3 units Down
3. Coordinate Rule: (x, y) → (x − 4, y − 3)
💡 Vector: ⟨−4, −3⟩ moves D(1,4) to D′(−3,1).
STATION 8 Translation (+3, −4)
3 pts
1. Type: Translation
2. Vector words: Slide 3 right and 4 down
3. Verification: (−4+3, 2−4) = (−1, −2) ✓
💡 Rule Check: Formula (x+3, y−4) correctly models all 4 vertices.
Transformations Gallery Walk • Teacher Answer Key Page 1 of 2
TEACHER REFERENCE • ANSWER KEY
TRANSFORMATION MYSTERY KEY
Stations 9–16 Solutions & Bonus Composite Challenge
Standard: CCSS.MATH.CONTENT.8.G.A.3
Rotation Centers: Origin (0,0)
STATION 9 Translation (−5, +1)
3 pts
1. Type: Translation
2. Vector Shift: 5 units Left, 1 unit Up
3. Algebraic Rule: (x, y) → (x − 5, y + 1)
💡 Check: (1, −4) → (1−5, −4+1) = (−4, −3).
STATION 10 Horizontal Slide (−6, 0)
3 pts
1. Type: Translation (Horizontal)
2. What happened to x: x decreased by 6 (shifted 6 left)
3. Algebraic Rule: (x, y) → (x − 6, y)
💡 Key Idea: y-coordinates stay constant because vertical shift is 0.
STATION 11 Rotation 90° Clockwise
3 pts
1. Center: Origin (0, 0)
2. Degrees & Direction: 90° Clockwise (or 270° CCW)
3. Algebraic Rule: (x, y) → (y, −x)
💡 Rule Check: (1, 2) → (2, −1) and (1, 5) → (5, −1).
STATION 12 Rotation 180° around Origin
3 pts
1. Type: Rotation
2. Which rotation: 180° rotation around (0,0)
3. Algebraic Rule: (x, y) → (−x, −y)
💡 Sign Rule: 180° turns invert both signs regardless of CW/CCW.
STATION 13 Rotation 90° CCW
3 pts
1. Type: Rotation
2. Degrees & Direction: 90° Counter-Clockwise
3. Algebraic Rule: (x, y) → (−y, x)
💡 Check: (2, 1) → (−1, 2) and (5, 1) → (−1, 5).
STATION 14 Rotation 180° Quadrilateral
3 pts
1. Type: Rotation
2. Center & Degrees: Center (0, 0), 180°
3. Algebraic Rule: (x, y) → (−x, −y)
💡 Check: (1, 1) → (−1, −1); (4, 1) → (−4, −1); (3, 3) → (−3, −3).
STATION 15 Rotation 90° Clockwise
3 pts
1. Type: Rotation
2. Confirmation: 90° Clockwise around origin
3. Algebraic Rule: (x, y) → (y, −x)
💡 Check: (−3, 2) → (2, −(−3)) = (2, 3) ✓.
★ STATION 16 Composite Motion Key
5 pts
Step 1: Reflection across x-axis (y = 0)
(x, y) → (x, −y): (1,1)→(1,−1)
Step 2: Translation 4 units Left
(x, y) → (x − 4, y): (1,−1)→(−3,−1)
Combined Rule: (x, y) → (x − 4, −y)
💡 Note: Performing the translation first, then reflecting over x-axis yields identical final points.
Rigid Motion Rules Summary: Reflect x: (x,−y) Reflect y: (−x,y) Rot 90° CW: (y,−x) Rot 180°: (−x,−y) Rot 90° CCW: (−y,x)
Page 2 of 2
Transformation Mystery Exit Ticket EXIT TICKET Rigid Transformations
TRANSFORMATION MYSTERY
Name:
Date:
Per:
1. Triangle ABC has vertices A(2, 4), B(5, 4), and C(2, 1). If its image has vertices A′(−2, 4), B′(−5, 4), and C′(−2, 1), what transformation occurred?
Reflection across the y-axis Reflection across the x-axis Translation 4 units left
2. Point P(−3, 5) is translated using the rule (x, y) → (x + 6, y − 2).
What are the coordinates of P′?
P′ ( , )
3. A figure is rotated 90° clockwise about the origin (0, 0).
Complete the algebraic rule:
(x, y) → ( , )
4. Error Analysis: Jordan claims that rotating 180° around (0, 0) and reflecting over both axes produces the same image. Is Jordan correct? Why or why not?
How confident do you feel with rigid transformations?
1 (Need Help) 2 (Getting There) 3 (Got It) 4 (Can Teach It)
✂ Cut Here (2 Tickets Per Page)
EXIT TICKET Rigid Transformations
TRANSFORMATION MYSTERY
Name:
Date:
Per:
1. Triangle ABC has vertices A(2, 4), B(5, 4), and C(2, 1). If its image has vertices A′(−2, 4), B′(−5, 4), and C′(−2, 1), what transformation occurred?
Reflection across the y-axis Reflection across the x-axis Translation 4 units left
2. Point P(−3, 5) is translated using the rule (x, y) → (x + 6, y − 2).
What are the coordinates of P′?
P′ ( , )
3. A figure is rotated 90° clockwise about the origin (0, 0).
Complete the algebraic rule:
(x, y) → ( , )
4. Error Analysis: Jordan claims that rotating 180° around (0, 0) and reflecting over both axes produces the same image. Is Jordan correct? Why or why not?
How confident do you feel with rigid transformations?
1 (Need Help) 2 (Getting There) 3 (Got It) 4 (Can Teach It)