MIA · Mixed set · Unit 1

1. 1.

   Plot and name the quadrant (or axis) of (4, 0).

   Answer. x-axis

   Use the signs of x and y.

2. 2.

   Which transformations are rigid: translation, reflection, rotation, dilation?

   Answer. translation, reflection, rotation (not dilation)

   translation, reflection, rotation (not dilation)

3. 3.

   Rotate point A(4, 2) 90° counterclockwise about the origin. Image?

   Answer. (-2, 4)

   (x, y) → (−y, x) for 90° CCW: (-2, 4).

4. 4.

   Point A(1, 1) is translated 3 units right, then reflected over the y-axis. Final image?

   Answer. (-4, 1)

   After translate: (4, 1). After reflect over y-axis: (-4, 1).

5. 5.

   Can 5, 7, 10 be the side lengths of a triangle? Write a complete answer — Grace will compare with a partner.

   Answer. yes

   5+7=12 > 10.

6. 6.

   A reflection maps a figure over the y-axis. Are corresponding angles congruent? Write a complete answer — Luis will compare with a partner.

   Answer. yes

   yes

7. 7.

   Translate point A(4, 4) by (+1, -2). What are the image coordinates? Write a complete answer — Nora will compare with a partner.

   Answer. (5, 2)

   A' = (4+1, 4+-2) = (5, 2).

8. 8.

   Point A(3, 2) is translated 3 units right, then reflected over the y-axis. Final image? Write a complete answer — Ava will compare with a partner.

   Answer. (-6, 2)

   After translate: (6, 2). After reflect over y-axis: (-6, 2).

9. 9.

   In which quadrant is the point (−5, −3)? Write a complete answer — Mei will compare with a partner.

   Answer. Quadrant III

   x is negative and y is negative → Quadrant III.

10. 10.

    Which transformations are rigid: translation, reflection, rotation, dilation? Write a complete answer — Mei will compare with a partner.

    Answer. translation, reflection, rotation (not dilation)

    translation, reflection, rotation (not dilation)

11. 11.

    Think

    Grace tried this problem:
    Reflect point A(3, 4) over the y-axis. Image coordinates?
    Grace wrote (-2, 4). That is not correct. What is the right answer?

    Answer. (-3, 4)

    Grace’s answer (-2, 4) is off. Reflection over y-axis: (x, y) → (−x, y).

12. 12.

    Think

    Theo tried this problem:
    Point A(3, 1) is translated 3 units right, then reflected over the y-axis. Final image?
    Theo wrote (-5, 1). That is not correct. What is the right answer?

    Answer. (-6, 1)

    Theo’s answer (-5, 1) is off. After translate: (6, 1). After reflect over y-axis: (-6, 1).

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