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Answer:

  1. 2/3; (x, y) ⇒ (2/3x, 2/3y)
  2. 1/2; (x, y) ⇒ (1/2x, 1/2y)
  3. 7/8; (x, y) ⇒ (7/8x, 7/8y)
  4. 1/4; (x, y) ⇒ (1/4x, 1/4y)

Step-by-step explanation:

For dilations about the origin, such as these, the scale factor is always the ratio of any image point coordinate* to the corresponding preimage point coordinate. If the scale factor is k, the transformation can be written as ...

  (x, y) ⇒ (kx, ky)

__

  S(9,12) ⇒ S'(6, 8) . . . . scale factor is 6/9 = 2/3; relation is (x, y) ⇒ (2/3x, 2/3y)

  U(8, 18) ⇒ U'(4, 9) . . . scale factor is 4/8 = 1/2; relation is (x, y) ⇒ (1/2x, 1/2y)

  I(0,8) ⇒ I'(0, 7) . . . scale factor is 7/8; relation is (x, y) ⇒ (7/8x, 7/8y)

  X(16, 8) ⇒ X'(4, 2) . . . scale factor is 2/8 = 1/4; relation is (x, y) ⇒ (1/4x, 1/4y)

_____

* The origin is the one invariant point in a dilation, so the chosen coordinate cannot be zero.

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