Skills · Geometry · Rigid Motions

Translations

Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.

Problem types

Sample Sheet · Level 1

  1. point A at (−2, 3), point A′ at (−3, 5)AA′−6−6−4−4−2−2224466xy
    A translation takes A to A′. Write the translation as a vector.
  2. point A at (5, 5)A−6−6−4−4−2−2224466xy
    Translate A 3 units left and 1 unit down. Find A′.
  3. point A at (1, 2), point A′ at (4, 6)AA′−6−6−4−4−2−2224466xy
    A translation takes A to A′. Write the translation as a vector.
  4. point A at (1, 5)A−6−6−4−4−2−2224466xy
    Translate A 1 unit right and 4 units down. Find A′.
  5. point A at (−1, 3), point A′ at (−3, 4)AA′−6−6−4−4−2−2224466xy
    A translation takes A to A′. Write the translation as a vector.
  6. point A at (−4, 5)A−6−6−4−4−2−2224466xy
    Translate A 3 units right and 4 units down. Find A′.
  7. point A at (2, 3), point A′ at (1, −1)AA′−6−6−4−4−2−2224466xy
    A translation takes A to A′. Write the translation as a vector.
  8. point A at (−1, 3)A−6−6−4−4−2−2224466xy
    Translate A 2 units right and 4 units down. Find A′.

Answer key

  1. ⟨−1, 2⟩
  2. (2, 4)
  3. ⟨3, 4⟩
  4. (2, 1)
  5. ⟨−2, 1⟩
  6. (−1, 1)
  7. ⟨−1, −4⟩
  8. (1, −1)

Sample Sheet · Level 3

  1. A translation takes A(−2, −3) to A′(3, −4). Write the translation as a vector.
  2. Translate A(5, 1) by the vector ⟨−1, −2⟩. Find A′.
  3. A translation takes A(−2, 5) to A′(−4, 1). Write the translation as a vector.
  4. triangle ABC with A at (5, 4), B at (4, 1), C at (3, 4)ABC−6−6−4−4−2−2224466xy
    Translate △ABC by the vector ⟨−2, −3⟩. Find B′.
  5. A translation by ⟨4, −5⟩ takes A to A′(6, −6). Find A.
  6. triangle ABC with A at (4, −1), B at (1, −3), C at (3, −5)ABC−6−6−4−4−2−222466xy
    Translate △ABC by the vector ⟨2, −1⟩. Find B′.
  7. A translation by ⟨−3, 1⟩ takes A to A′(3, −5). Find A.
  8. Translate A(−2, −2) by the vector ⟨3, −1⟩. Find A′.

Answer key

  1. ⟨5, −1⟩
  2. (4, −1)
  3. ⟨−2, −4⟩
  4. (2, −2)
  5. (2, −1)
  6. (3, −4)
  7. (6, −6)
  8. (1, −3)

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