Question

1. which is a true statement about dilations?

a. a dilation sometimes changes the
orientation of the vertices.
b. a dilation always preserves congruence.
c. a dilation sometimes enlarges a figure.
d. a dilation always changes the orientation of
a figure.

Explanation:

• Option A: Dilations do not change the orientation of vertices, so A is false.
• Option B: Dilations change the size (scale factor not 1), so they don't preserve congruence (congruent figures have same size/shape), so B is false.
• Option C: A dilation with a scale factor greater than 1 enlarges the figure, and with 0 - 1 shrinks it. So it sometimes enlarges (when scale factor > 1), so C is true.
• Option D: Dilations do not change the orientation of the figure, so D is false.

Answer:

C. A dilation sometimes enlarges a figure.