Question

1. a polygon is transformed by (x,y)→(5x,5y). which statement is true? a. the image is congruent to the original polygon. b. the image is smaller than the original. c. the image is larger than the original. d. the image is not similar to the original. 4. if trapezoid efgh is transformed by (x,y)→(⅓ x, ⅓ y), which is true about the side lengths of the image?

Explanation:

Step1: Recall transformation rule

The transformation $(x,y)\to(5x,5y)$ is a dilation with a scale - factor of 5. For a dilation with scale - factor $k$, if $k > 1$, the image is larger than the original. For the transformation $(x,y)\to(\frac{1}{3}x,\frac{1}{3}y)$, the scale - factor $k=\frac{1}{3}<1$, so the image is smaller than the original.

Step2: Analyze similarity and congruence

A dilation creates a similar figure. If the scale - factor $k = 1$, the figures are congruent. Since the scale - factors in the given transformations are not 1, the images are not congruent to the original. And all dilations create similar figures.

Answer:

1. A. The image is larger than the original.
2. B. The image is smaller than the original.