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. to verify that the transformation is a dilation, jeremy should also check which of the following? select three options. qb = (1/2)qe qc = cf de = 2ab ac = (1/2)ef if bc = 2.25, then ef = 2.25

Explanation:

A dilation preserves shape (similarity) with a scale factor. Given QA=AD=4, QD=QA+AD=8, so scale factor from small to large triangle is QD/QA=2.

• QB=1/2 QE: QE=QB+BE, so QB/QE=1/2 means scale factor 2 (correct).
• DE=2AB: Corresponding sides scale by 2 (correct).
• AC=1/2 EF: Corresponding sides scale by 2 (correct).

Other options (QC=CF, EF=BC) imply scale factor 1, which contradicts QA≠QD.

Answer:

A. QB = 1/2 QE, C. DE = 2AB, D. AC = 1/2 EF