Question

Jeremy wants to verify that the transformation shown is a dilation. He finds the lengths of segments QA and AD to be 4 units.

Point Q is the center of dilation. Triangle A B C is dilated to create triangle D E F. The length of Q A is 4 and the length of A D is 4.

To verify that the transformation is a dilation, Jeremy should also check which of the following? Select three options.

QB = One-halfQE
QC = CF
DE = 2AB
AC = One-halfEF
if BC = 2.25, then EF = 2.25

Answer 1

Answer:
- QB = one-half QE
- QC = CF
- DE = 2AB

Reason: QA = AD implies (k − 1)QA = QA so k = 2. For a dilation of factor 2 about Q: QE = 2·QB (so QB = 1/2 QE), QF = 2·QC so CF = QF − QC = 2QC − QC = QC, and each side is doubled (DE = 2·AB). The other two options are false (AC does not correspond to EF, and EF would be 2·BC, not equal to BC).