Skills · Geometry · Similarity

Dilations and scale factor

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 (−6, 4)A−6−6−4−4−2−2224466xy
    Dilate A by a scale factor of 3, centered at the origin. Find A′.
  2. triangle ABC and its image A′B′C′: BC 30, B′C′ ?ABCA′B′C′30?
    △ABC is dilated by a scale factor of 12. Find B′C′.
  3. point A at (5, 2)A−6−6−4−4−2−2224466xy
    Dilate A by a scale factor of 3, centered at the origin. Find A′.
  4. triangle ABC and its image A′B′C′: BC 5, B′C′ ?ABCA′B′C′5?
    △ABC is dilated by a scale factor of 4. Find B′C′.
  5. triangle ABC and its image A′B′C′: BC 30, B′C′ 20ABCA′B′C′3020
    △A′B′C′ is a dilation of △ABC. Find the scale factor.
  6. triangle ABC and its image A′B′C′: AB 9, A′B′ 3ABCA′B′C′93
    △A′B′C′ is a dilation of △ABC. Find the scale factor.
  7. triangle ABC and its image A′B′C′: AB 8, A′B′ ?ABCA′B′C′8?
    △ABC is dilated by a scale factor of 2. Find A′B′.
  8. triangle ABC and its image A′B′C′: BC 12, B′C′ 36ABCA′B′C′1236
    △A′B′C′ is a dilation of △ABC. Find the scale factor.

Answer key

  1. (−18, 12)
  2. 15 units
  3. (15, 6)
  4. 20 units
  5. 23
  6. 13
  7. 16 units
  8. 3

Sample Sheet · Level 3

  1. Dilate A(2, 8) by a scale factor of 2, centered at P(4, 2). Find A′.
  2. Dilate A(4, −7) by a scale factor of 2, centered at the origin. Find A′.
  3. triangle ABC and its image A′B′C′: AC ?, A′C′ 14ABCA′B′C′?14
    △A′B′C′ is △ABC dilated by a scale factor of 12. Find AC.
  4. Dilate A(−8, 2) by a scale factor of 32, centered at the origin. Find A′.
  5. triangle ABC and its image A′B′C′: BC 24, B′C′ 18ABCA′B′C′2418
    △A′B′C′ is a dilation of △ABC. Find the scale factor.
  6. triangle ABC and its image A′B′C′: AB 22, A′B′ 11ABCA′B′C′2211
    △A′B′C′ is a dilation of △ABC. Find the scale factor.
  7. triangle ABC and its image A′B′C′: AB 8, A′B′ ?ABCA′B′C′8?
    △ABC is dilated by a scale factor of 14. Find A′B′.
  8. Dilate A(2, −3) by a scale factor of 3, centered at P(1, 1). Find A′.

Answer key

  1. (0, 14)
  2. (8, −14)
  3. 28 units
  4. (−12, 3)
  5. 34
  6. 12
  7. 2 units
  8. (4, −11)

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