Skills · Geometry · Rigid Motions

Reflections

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 (1, 2)A−6−6−4−4−2−2224466xy
    Reflect A over the x-axis. Find A′.
  2. point A at (−3, −2), the line y = x drawn dashedA−6−6−4−4−2−2224466xy
    Reflect A over the line y = x. Find A′.
  3. point A at (−3, −4)A−6−6−4−4−2−2224466xy
    Reflect A over the y-axis. Find A′.
  4. point A at (−5, 3), the line y = x drawn dashedA−6−6−4−4−2−2224466xy
    Reflect A over the line y = x. Find A′.
  5. point A at (−5, 1)A−6−6−4−4−2−2224466xy
    Reflect A over the x-axis. Find A′.
  6. point A at (−4, −1), the line y = x drawn dashedA−6−6−4−2−2224466xy
    Reflect A over the line y = x. Find A′.
  7. point A at (−2, 5)A−6−6−4−4−2−2224466xy
    Reflect A over the y-axis. Find A′.
  8. point A at (1, −3), the line y = x drawn dashedA−6−6−4−4−2−2224466xy
    Reflect A over the line y = x. Find A′.

Answer key

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

Sample Sheet · Level 3

  1. Reflect A(−1, −2) over the line x = −2. Find A′.
  2. triangle ABC with A at (5, −3), B at (2, −4), C at (2, −1)ABC−6−6−4−4−2−224466xy
    Reflect △ABC over the x-axis. Find A′.
  3. Reflect A(4, 3) over the line x = 4. Find A′.
  4. triangle ABC with A at (2, 4), B at (3, 1), C at (5, 2), the line y = −1 drawn dashedABC−6−6−4−4−2−2224466xy
    Reflect △ABC over the line y = −1. Find A′.
  5. Reflect A(−3, −1) over the x-axis. Find A′.
  6. Reflect A(4, 2) over the line y = −x. Find A′.
  7. Reflect A(−5, 6) over the y-axis. Find A′.
  8. Is A′(5, 6) the reflection of A(−5, 6) over the x-axis, the y-axis, y = x, y = −x, or none of them?

Answer key

  1. (−3, −2)
  2. (5, 3)
  3. (4, 3)
  4. (2, −6)
  5. (−3, 1)
  6. (−2, −4)
  7. (5, 6)
  8. the y-axis

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