UA · Unit 1 review

1. 1.

   Plot and name the quadrant (or axis) of (-2, -1).

   Answer. Quadrant III

   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(3, 3) 90° counterclockwise about the origin. Image?

   Answer. (-3, 3)

   (x, y) → (−y, x) for 90° CCW: (-3, 3).

4. 4.

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

   Answer. (-4, 3)

   After translate: (4, 3). After reflect over y-axis: (-4, 3).

5. 5.

   Can 5, 9, 12 be the side lengths of a triangle? Write a complete answer — Theo will compare with a partner.

   Answer. yes

   5+9=14 > 12.

6. 6.

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

   Answer. yes

   yes

7. 7.

   Translate point A(4, 1) by (+1, +0). What are the image coordinates? Write a complete answer — Owen will compare with a partner.

   Answer. (5, 1)

   A' = (4+1, 1+0) = (5, 1).

8. 8.

   Point A(1, 1) is translated 1 units right, then reflected over the y-axis. Final image? Write a complete answer — Ava will compare with a partner.

   Answer. (-2, 1)

   After translate: (2, 1). After reflect over y-axis: (-2, 1).

9. 9.

   In which quadrant is the point (1, 3)? Write a complete answer — Elena will compare with a partner.

   Answer. Quadrant I

   x is positive and y is positive → Quadrant I.

10. 10.

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

    Answer. translation, reflection, rotation (not dilation)

    translation, reflection, rotation (not dilation)

11. 11.

    Think

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

    Answer. (-2, 2)

    Luis’s answer (-3, 2) is off. Reflection over y-axis: (x, y) → (−x, y).

12. 12.

    Think

    Priya tried this problem:
    Point A(3, 3) is translated 1 units right, then reflected over the y-axis. Final image?
    Priya wrote (-8, 3). That is not correct. What is the right answer?

    Answer. (-4, 3)

    Priya’s answer (-8, 3) is off. After translate: (4, 3). After reflect over y-axis: (-4, 3).

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