Two transformations are performed on a figure on a coordinate plane. The first transformation is a translation 10 units to the right. Which second transformation will result in an figure that is 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 10 units to the right. Which second transformation will result in an figure that is 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. Translation does not affect similarity, so the figure remains similar to the original after being translated 10 units to the right. A dilation with a scale factor other than 1 will change the size of the figure, making it similar but not congruent to the original. Choosing a dilation with a scale factor less than 1 (option d) will shrink the figure, while choosing a dilation with a scale factor greater than 1 will enlarge the figure. Rotations and dilations with the origin not being the center of dilation will also change the position of the figure, making it not similar to the original.