Question

a sequence of transformations is described below.

• a translation
• a dilation about a point p
• another translation
• a rotation about the point p

which of the following must be preserved under this sequence of transformations?
choose 1 answer:
a angle measures only
b segment lengths only
c both angle measures and segment lengths
d neither angle measures nor segment lengths

Explanation:

Step1: Analyze each transformation

• Translation: Preserves both angle measures and segment lengths (rigid transformation).
• Dilation: Preserves angle measures but changes segment lengths (non - rigid, scale factor ≠ 1).
• Another translation: Preserves both angle measures and segment lengths.
• Rotation: Preserves both angle measures and segment lengths (rigid transformation).

Step2: Determine preserved property

Since dilation changes segment lengths, segment lengths are not preserved. But angle measures are preserved under translation, dilation, and rotation. So only angle measures are preserved.

Answer:

A. Angle measures only