Rigid Transformations

Moving a shape without changing it.

12 problems · about 21 minutes · G-CO.A.2, G-CO.A.5

What this lesson teaches

The student performs and describes translations, reflections and rotations.

Straightforward practice. Get the method working first.

5 problems

Reflect (6, 2) across the y-axis. New x-coordinate?
Answer -6
Why −6.
What does a rigid transformation preserve?
Answer Both lengths and angles.
Why Size and shape are unchanged.
Translate (1, 1) up by 5. New y-coordinate?
Answer 6
Why 1 + 5.
Reflect (7, 2) across the y-axis. New x-coordinate?
Answer -7
Why x flips.
Rotate (3, 5) by 180° about the origin. New x-coordinate?
Answer -3
Why Both coordinates negate.

The same ideas with more to keep track of.

3 problems

Same rotation. New y-coordinate?
Answer -5
Why Both negate.
A shape has side 8. After a translation, what is that side length?
Answer 8
Why Rigid means unchanged.
Which transformation reverses orientation? 1 translation, 2 reflection.
Answer 2
Why Think of a mirrored hand.

Mixed problems. Work out what kind of question it is before you start.

4 problems

Match each transformation with its effect on a point.
Answer Reflect across the x-axis → The y-coordinate negates; Reflect across the y-axis → The x-coordinate negates; Rotate 180 degrees about the origin → Both coordinates negate
Why A half turn does both flips at once.
Translate (5, 5) left by 8. New x-coordinate?
Answer -3
Why 5 − 8.
The Slide: Translate (2, 5) right by 4. What is the new x-coordinate?
Answer 6
Why 6.
The Flip: Reflect (4, 3) across the x-axis. What is the new y-coordinate?
Answer -3
Why −3.