L2 · Single rigid transformations in the coordinate plane

1. 1.

   Translate point A(3, 2) by (+3, -1). What are the image coordinates?

   Answer. (6, 1)

   A' = (3+3, 2+-1) = (6, 1).

2. 2.

   Reflect point A(1, 1) over the y-axis. Image coordinates?

   Answer. (-1, 1)

   Reflection over y-axis: (x, y) → (−x, y).

3. 3.

   Rotate point A(4, 4) 90° counterclockwise about the origin. Image?

   Answer. (-4, 4)

   (x, y) → (−y, x) for 90° CCW: (-4, 4).

4. 4.

   Translate point A(1, 2) by (+3, +1). What are the image coordinates?

   Answer. (4, 3)

   A' = (1+3, 2+1) = (4, 3).

5. 5.

   Reflect point A(4, 3) over the y-axis. Image coordinates? Write a complete answer — Priya will compare with a partner.

   Answer. (-4, 3)

   Reflection over y-axis: (x, y) → (−x, y).

6. 6.

   Rotate point A(4, 1) 90° counterclockwise about the origin. Image? Write a complete answer — Malik will compare with a partner.

   Answer. (-1, 4)

   (x, y) → (−y, x) for 90° CCW: (-1, 4).

7. 7.

   Translate point A(3, 2) by (+2, +0). What are the image coordinates? Write a complete answer — Mei will compare with a partner.

   Answer. (5, 2)

   A' = (3+2, 2+0) = (5, 2).

8. 8.

   Reflect point A(3, 3) over the y-axis. Image coordinates? Write a complete answer — Jonah will compare with a partner.

   Answer. (-3, 3)

   Reflection over y-axis: (x, y) → (−x, y).

9. 9.

   Rotate point A(1, 4) 90° counterclockwise about the origin. Image? Write a complete answer — Luis will compare with a partner.

   Answer. (-4, 1)

   (x, y) → (−y, x) for 90° CCW: (-4, 1).

10. 10.

    Translate point A(2, 3) by (+1, -2). What are the image coordinates? Write a complete answer — Jonah will compare with a partner.

    Answer. (3, 1)

    A' = (2+1, 3+-2) = (3, 1).

11. 11.

    Think

    Grace tried this problem:
    Reflect point A(2, 1) over the y-axis. Image coordinates?
    Grace wrote (2, 1). That is not correct. What is the right answer?

    Answer. (-2, 1)

    Grace’s answer (2, 1) is off. Reflection over y-axis: (x, y) → (−x, y).

12. 12.

    Think

    Mei tried this problem:
    Rotate point A(2, 4) 90° counterclockwise about the origin. Image?
    Mei wrote (-8, 2). That is not correct. What is the right answer?

    Answer. (-4, 2)

    Mei’s answer (-8, 2) is off. (x, y) → (−y, x) for 90° CCW: (-4, 2).

Original extra practice. Keys are computed from the items, not guessed.