Cogito
Grade 8 Math · Chapter 1 · Lesson 1
Moving a Shape Without Changing It
Slides, flips, and turns.
8 problems · about 18 minutes · 8.G.A.1
What this lesson teaches
The child describes translations, reflections, and rotations and their effect on a figure.
- Translation slides, reflection flips, rotation turns.
- All three keep every length and every angle.
- Only position and facing change.
Warm Up
Straightforward practice. Get the method working first.
4 problems(2, 9) reflected across the vertical axis. New first coordinate?
Answer -2
Why (−2, 9).
What does a rigid motion preserve?
Answer Lengths and angles.
Why Lengths and angles survive; position does not.
(1, 3) translated 5 right. New first coordinate?
Answer 6
Why 1 + 5.
(6, 2) reflected across the vertical axis. New first coordinate?
Answer -6
Why Sign flips.
Build It Up
The same ideas with more to keep track of.
2 problems(3, 8) reflected across the horizontal axis. New second coordinate?
Answer -8
Why Second coordinate flips.
Does a rigid motion change side lengths?
Answer No.
Why That is what rigid means.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Slide: A point at (2, 5) is translated 3 right. What is its new first coordinate?
Answer 5
Why (5, 5).
The Flip: A point at (4, 7) is reflected across the vertical axis. What is its new first coordinate?
Answer -4
Why (−4, 7).