Question

Suppose one figure is mapped to a similar 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? would it be dilation?

Answer 1

Yes, in this case, a dilation transformation must occur.

When you have two similar figures, one figure (the image) is a scaled version of the other (the preimage). If the lengths of the sides of the similar figure are twice the lengths of the corresponding sides of the original figure, then this implies a dilation with a scale factor of 2.

Dilation is a transformation that changes the size of a figure but retains its shape, and it operates from a fixed point (the center of dilation). In your scenario, the original figure is enlarged by a scale factor of 2, resulting in a figure that is similar to the original with all corresponding side lengths proportional. Thus, the transformation that occurs to map the preimage to the image is indeed a dilation.

Answer 2

Thank you

Answer 3

You're welcome! If you have any more questions or need further clarification, feel free to ask. Happy studying!