Two transformations are performed on a figure on a coordinate plane. The first transformation is a translation of 10 units to the right. Which second transformation will result in a figure similar to, but not congruent to, the original figure?

Question

Two transformations are performed on a figure on a coordinate plane. The first transformation is a translation of 10 units to the right. Which second transformation will result in a figure similar to, but not congruent to, the original figure?

A. A clockwise rotation of 90° about the center.

B. A clockwise rotation of 180° about the center.

C. A dilation by a scale factor of 1 with the origin as the center of dilation.

D. A dilation by a scale factor of 1/2 with the origin as the center of dilation.

Answer 1

D. A dilation by a scale factor of 1/2 with the origin as the center of dilation. Translating the figure to the right does not change its shape, but dilating it with a scale factor of 1/2 will make it smaller, resulting in a figure similar to the original but not congruent. Rotations do not change the size of a figure, so options A and B would result in congruent figures. Option C would result in the same figure, since a scale factor of 1 does not change its size or shape.