Question

Quadrilateral EFGH was dilated by a scale factor of 2 from the center (1, 0) to create E′F′G′H′. Which characteristic of dilations compares segment H′G′ to segment HG? A) A segment that passes through the center of dilation in the pre-image continues to pass through the center of dilation in the image. B) A segment in the image has the same length as its corresponding segment in the pre-image. C) A segment that passes through the center of dilation in the pre-image does not pass through the center of dilation in the image. D) A segment that does not pass through the center of dilation in the pre-image is parallel to its corresponding segment in the image.

Answer 1

A segment in the image has the same length as its corresponding segment in the pre-image.

Step-by-step explanation:

To compare segment H′G′ to segment HG, we need to understand the characteristics of dilations. One characteristic of dilations is that a segment that passes through the center of dilation in the pre-image continues to pass through the center of dilation in the image, so this is not the characteristic we are looking for (option A). Another characteristic is that a segment in the image has the same length as its corresponding segment in the pre-image, which means that segment H′G′ has the same length as segment HG (option B). Therefore, the characteristic that compares segment H′G′ to segment HG is option B.