Question

a sequence of transformations is described below.

• a dilation about a point ( p )
• a translation
• a reflection over a line ( overleftrightarrow{qr} )
• a dilation about the point ( r )

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 Dilation Effect

Dilation changes segment lengths (scales them) but preserves angle measures.

Step2: Analyze Translation/Reflection

Translation and reflection are rigid transformations, preserving both angle measures and segment lengths.

Step3: Overall Effect

Since there are dilations (which don't preserve segment lengths) but all transformations (including dilations) preserve angle measures, only angle measures are preserved.

Answer:

A. Angle measures only