Question

multiple choice 1 point
which is a true statement about dilations?
a dilation always preserves congruence.
a dilation sometimes enlarges a figure.
a dilation sometimes changes the orientation of the vertices.
a dilation always changes the orientation of a figure.
clear my selection

Explanation:

• Option A: A dilation changes the size of a figure (unless the scale factor is \(1\)). Congruent figures have the same size and shape. Since dilation usually changes the size, it does not always preserve congruence.
• Option B: If the scale factor \(k> 1\), a dilation enlarges a figure. If \(0 < k<1\), it reduces the figure. So, a dilation sometimes enlarges a figure.
• Option C and D: A dilation is a similarity transformation that maps a pre - image to an image. The orientation of the vertices (the order of the vertices when going around the figure) is preserved.

Answer:

B. A dilation sometimes enlarges a figure.