Question

a sequence of transformations is described below.

• a dilation about a point ( p )
• a rotation about another point ( q )
• a vertical stretch about the horizontal line ( overleftrightarrow{pq} )
• a reflection over ( overleftrightarrow{pq} )

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:

1. Analyze each transformation:

• Dilation: Changes segment lengths (scales them) but preserves angle measures.
• Rotation: Preserves both angle measures and segment lengths (rigid transformation).
• Vertical stretch: Changes segment lengths (stretches vertically) but preserves angle measures (since it's a stretch along a horizontal line, angles remain the same as the horizontal and vertical components' ratio changes, but the angle between lines is preserved in terms of measure).
• Reflection: Preserves both angle measures and segment lengths (rigid transformation).

1. Overall, since dilation and vertical stretch change segment lengths, segment lengths are not preserved. However, angle measures are preserved through all these transformations (dilation, rotation, vertical stretch, reflection all keep angle measures the same). So only angle measures are preserved.

Answer:

A. Angle measures only