Skills · Geometry · Rigid Motions

Compositions of rigid motions

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 (5, 3)A−6−6−4−4−2−2224466xy
    Reflect A over the y-axis, then translate it by the vector ⟨4, −2⟩. Find A″.
  2. point A at (−2, 3)A−6−6−4−4−2−2224466xy
    Reflect A over the y-axis, then translate it by the vector ⟨−1, −4⟩. Find A″.
  3. point A at (−5, 3)A−6−6−4−4−2−2224466xy
    Reflect A over the y-axis, then translate it by the vector ⟨1, 3⟩. Find A″.
  4. point A at (3, −1)A−6−6−4−4−2−2224466xy
    Reflect A over the y-axis, then translate it by the vector ⟨−3, 4⟩. Find A″.
  5. point A at (−4, 2)A−6−6−4−4−2−2224466xy
    Translate A by the vector ⟨−2, −1⟩, then reflect over the x-axis. Find A″.
  6. point A at (−3, −1)A−6−6−4−4−2−2224466xy
    Reflect A over the x-axis, then translate it by the vector ⟨1, −4⟩. Find A″.
  7. point A at (5, −1)A−6−6−4−4−2−2224466xy
    Reflect A over the y-axis, then translate it by the vector ⟨−1, −2⟩. Find A″.
  8. point A at (−5, −3)A−6−6−4−4−2−2224466xy
    Reflect A over the x-axis, then translate it by the vector ⟨−1, −2⟩. Find A″.

Answer key

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

Sample Sheet · Level 3

  1. Reflect A(2, −1) over the x-axis, then reflect over the y-axis. Find A″.
  2. Reflect A(1, 4) over the x-axis, then translate it by the vector ⟨−3, 2⟩. Find A″.
  3. Translate A(3, −6) by the vector ⟨1, 0⟩, then reflect over the x-axis. Find A″.
  4. Rotate A(−2, 1) 90° about the origin, then translate it by the vector ⟨5, −3⟩. Find A″.
  5. Translate A(5, −3) by the vector ⟨0, 5⟩, then reflect over the y-axis. Find A″.
  6. triangle ABC with A at (5, 4), B at (2, 4), C at (2, 1), the line y = −x drawn dashedABC−6−6−4−4−2−2224466xy
    Reflect △ABC over the y-axis, then reflect over the line y = −x. Find A″.
  7. Rotate A(3, −2) 180° about the origin, then translate it by the vector ⟨5, −3⟩. Find A″.
  8. triangle ABC with A at (1, 2), B at (3, 1), C at (3, 4)ABC−6−6−4−4−2−2224466xy
    Reflect △ABC over the y-axis, then reflect over the x-axis. Find C″.

Answer key

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

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