UA · Unit 2 review

1. 1.

   Dilate point P(2, 3) about the origin by scale factor 3. Image?

   Answer. (6, 9)

   (x, y) → (3x, 3y) = (6, 9).

2. 2.

   Point P(3, 4) is dilated by 2 about the origin, then translated 3 units up. Final image?

   Answer. (6, 11)

   Dilate: (6, 8). Translate: (6, 11).

3. 3.

   Two parallel lines are cut by a transversal. One corresponding angle measures 40°. Find the other corresponding angle.

   Answer. 40°

   Corresponding angles are congruent.

4. 4.

   Two angles of a triangle measure 61° and 74°. Find the third angle.

   Answer. 45°

   61 + 74 + x = 180 → x = 45.

5. 5.

   Dilate point P(2, 3) about the origin by scale factor 3. Image? Write a complete answer — Jonah will compare with a partner.

   Answer. (6, 9)

   (x, y) → (3x, 3y) = (6, 9).

6. 6.

   Point P(2, 2) is dilated by 2 about the origin, then translated 3 units up. Final image? Write a complete answer — Jonah will compare with a partner.

   Answer. (4, 7)

   Dilate: (4, 4). Translate: (4, 7).

7. 7.

   Two parallel lines are cut by a transversal. One consecutive interior angle is 50°. Find the other. Then Sam needs 2 of that amount. What is the total they need?

   Answer. 260°

   Consecutive interior angles are supplementary: 180 − 50 = 130. Then multiply by 2: 260°.

8. 8.

   Two angles of a triangle measure 49° and 49°. Find the third angle. Then Grace needs 5 of that amount. What is the total they need?

   Answer. 410°

   49 + 49 + x = 180 → x = 82. Then multiply by 5: 410°.

9. 9.

   Dilate point P(5, 4) about the origin by scale factor 4. Image? Write a complete answer — Nora will compare with a partner.

   Answer. (20, 16)

   (x, y) → (4x, 4y) = (20, 16).

10. 10.

    Point P(1, 1) is dilated by 2 about the origin, then translated 3 units up. Final image? Write a complete answer — Mei will compare with a partner.

    Answer. (2, 5)

    Dilate: (2, 2). Translate: (2, 5).

11. 11.

    Think

    Luis tried this problem:
    Two parallel lines are cut by a transversal. One corresponding angle measures 45°. Find the other corresponding angle.
    Luis wrote 44°. That is not correct. What is the right answer?

    Answer. 45°

    Luis’s answer 44° is off. Corresponding angles are congruent.

12. 12.

    Think

    Ava tried this problem:
    Two angles of a triangle measure 31° and 31°. Find the third angle.
    Ava wrote 117°. That is not correct. What is the right answer?

    Answer. 118°

    Ava’s answer 117° is off. 31 + 31 + x = 180 → x = 118.

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