Cogito
Grade 8 Math · Chapter 1 · Lesson 3
What a Transformation Does to Coordinates
The rule behind the movement.
10 problems · about 19 minutes · 8.G.A.3
What this lesson teaches
The child predicts the coordinates of an image after a translation, reflection, or rotation.
- A translation adds the same amount to every point.
- A reflection flips the sign of one coordinate.
- A quarter turn about the origin swaps the coordinates and flips one sign.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Congruence: Congruent shapes, one side is 15. The matching side?
Answer 15
Why 15.
Review — Moving a Shape Without Changing It: (2, 9) reflected across the vertical axis. New first coordinate?
Answer -2
Why (−2, 9).
Review — Congruence: How is congruence defined?
Answer One can be carried onto the other by rigid motions.
Why Congruence is defined by a sequence of rigid motions.
Warm Up
Straightforward practice. Get the method working first.
3 problems(6, −2) translated 3 left. What is the new x?
Answer 3
Why (3, −2).
(1, 2) translated 5 up. What is the new y?
Answer 7
Why 2 + 5.
(−3, 4) reflected across the y-axis. What is the new x?
Answer 3
Why The sign of x flips.
Build It Up
The same ideas with more to keep track of.
2 problems(5, 0) reflected across the x-axis. What is the new y?
Answer 0
Why Zero has no sign to flip.
Does a translation change the size of a shape? 1 for yes, 0 for no.
Answer 0
Why Every corner moves the same amount.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Slide: (2, 5) is translated 4 right. What is the new x?
Answer 6
Why (6, 5).
The Flip: (3, 7) is reflected across the x-axis. What is the new y?
Answer -7
Why (3, −7).