Cogito
Geometry · Chapter 2 · Lesson 2
Transformations on Coordinates
What each motion does to a point.
11 problems · about 22 minutes · G-CO.A.2, G-CO.A.5
What this lesson teaches
The student applies transformation rules to coordinates.
- Translations add, reflections flip one sign, and a quarter turn swaps the coordinates.
- All three preserve lengths and angles.
- That preservation is exactly why the image is congruent to the original.
Warm Up
Straightforward practice. Get the method working first.
4 problems(7, 2) reflected across the x-axis. New y?
Answer -2
Why −2.
(2, 6) reflected across the x-axis. New y?
Answer -6
Why The sign of y flips.
(−3, 4) reflected across the y-axis. New x?
Answer 3
Why Flip the sign.
(1, 5) translated 4 up. New y?
Answer 9
Why 5 + 4.
Build It Up
The same ideas with more to keep track of.
3 problems(2, 3) rotated 90° anticlockwise. New x?
Answer -3
Why (x, y) goes to (−y, x).
Do rigid motions change side lengths? 1 for yes, 0 for no.
Answer 0
Why Rigid means unchanged.
Match each motion to its coordinate rule.
Answer Reflect across the y-axis → (−x, y); Reflect across the x-axis → (x, −y); Rotate 90° anticlockwise → (−y, x)
Why Only the rotation swaps the two coordinates.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problems(0, 4) rotated 180° about the origin. New y?
Answer -4
Why Both signs flip.
(6, 6) reflected across the line y = x. New x?
Answer 6
Why It already sits on the line.
Reflecting: (5, 2) reflected across the y-axis. What is the new x?
Answer -5
Why −5.
Translating: (4, 7) translated 3 left. What is the new x?
Answer 1
Why 1.