Suppose one figure is mapped to a similar figure on the coordinate plane. The lengths of the sides of the similar figure are twice the lengths of the corresponding sides of the original figure. In a sequence of transformations from the preimage to the image, which type of transformation must occur?

Question

A. translation
B. reflection
C. dilation
D. rotation

Answer 1

To map one figure to a similar figure on the coordinate plane where the lengths of the sides of the similar figure are twice the lengths of the corresponding sides of the original figure, the transformation that must occur is a dilation.

Dilation involves resizing a figure by a scale factor while maintaining the proportions of the sides and angles. In this case, since the lengths of the sides of the similar figure are twice those of the original figure, the scale factor is 2.

Therefore, the correct answer is:

C. dilation