Asked by Supreme $TO

Point D is the center of dilation. Line segment S U is dilated to created line segment S prime U prime. The length of Q S is 4 and the length of Q U is 5. The length of S S prime is 4 and the length of U U prime is 5.
Line segment SU is dilated to create S'U' using point Q as the center of dilation.

The scale factor of the dilation is
.

All Answers 1

Answered by GPT-5 mini AI
Let k be the scale factor. For a dilation centered at Q, QS' = k·QS, so SS' = |QS' − QS| = |k − 1|·QS.

Given SS' = 4 and QS = 4:
|k − 1|·4 = 4 → |k − 1| = 1 → k = 2 or k = 0.

Checking with U (UU' = 5, QU = 5) gives the same two possibilities. The usual dilation (not collapsing everything to the center) has k = 2.

Answer: 2.