Transformations Sequence Worksheet
Math 7 • Geometry Foundations
Sequences of Transformations
Tracking multi-step movements: slides, flips, and turns on the grid
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Transformation Quick Reference
1. Translation (Slide)
Slides points without turning or flipping.
Right (+x) / Left (−x) • Up (+y) / Down (−y)
2. Reflection (Flip)
Flips shape across a mirror line.
Over x-axis: (x, −y) • Over y-axis: (−x, y)
3. Rotation (Turn)
Turns around the origin point (0, 0).
Clockwise or Counterclockwise (90°, 180°)
Guided Walkthrough: Track One Key Point Strategy: Peak Check
x y 2 4 -4 -2 2 -2 A P(−3, 4) A' A'' P''(4, −4)
How does Figure A become Figure A''?
1st Move: Translate 7 units right
Peak (−3, 4) slides to (4, 4). The roof still points UP.
2nd Move: Reflect across x-axis
Flipping across the horizontal line sends (4, 4) down to (4, −4). Roof now points DOWN.
💡 Observation: Changing direction (pointing up vs down) means a flip happened!
1 Guided Problem: Two-Step Triangle Journey Complete each step below
x y 2 4 -4 -2 2 -2 B K(−1, 3) B'' K''(4, −3)
Follow the clues to map Triangle B onto Triangle B'':
Part A: Orientation Check
Corner K points UP at (−1, 3), but K'' points DOWN at (4, −3).
Which transformation flips the shape upside down?
Reflect over x-axis Translation only
Part B: Counting the Movement
Notice the x-coordinate shifted from x = −1 to x = 4.
1. Distance slid horizontally: _______ units right
2. Line of reflection: across the _______ - axis
Complete 2-step sequence statement:
1st: ___________________________________ , 2nd: ___________________________________
Unit: Congruence & Transformations Page 1 of 2 Turn over for Test-Ready Practice ➔
Test Prep • Standard Practice
Independent Practice
Pro-Tip: Test one vertex on each answer choice!
2
Pentagon Sequence Challenge
Multiple Choice
In the diagram below, figures A and A'' are congruent. Which sequence of transformations can be performed on figure A to show that the figures are congruent?
x y 2 4 6 -6 -4 -2 2 4 -2 -4 A A''
A Translate figure A 7 units right. Then reflect figure A' across the x-axis.
B Translate figure A 5 units down. Then translate figure A' 7 units to the right.
C Reflect figure A across the y-axis. Then translate figure A' 5 units down.
D Rotate figure A 90° counterclockwise around origin. Then reflect across x-axis.
Clue: Peak (−3, 4). If moved 7 right: −3 + 7 = 4. Does the roof point up or down in A''?
My Answer: [ ]
3
Congruent Triangles Multi-Select
Choose ALL correct
In the diagram, \(\Delta QRS \cong \Delta TUV\). Which sequences of transformations can be performed on \(\Delta QRS\) to show that the triangles are congruent?
x y 2 4 -4 -2 2 4 -2 S R Q V U T
A Reflect across x-axis. Then across y-axis. Then across x-axis.
B Reflect \(\Delta QRS\) across the y-axis.
C Rotate 90° clockwise around origin. Then reflect across y-axis.
D Rotate 180° around origin. Then reflect across the x-axis.
E Translate \(\Delta QRS\) 4 units to the left.
Reflection: Explain Why
In Question 3, why does option B work, but option E (translate 4 left) fails?
Transformations & Coordinate Geometry Page 2 of 2 Great job showing your work!
