Question

Spiral review the segment with endpoints (0,8) and (−6,0) is dilated to a segment with endpoints (0, 6) and (−4.5,0) . what is the scale factor of the dilatspiral review the segment with endpoints (0,8) and (−6,0) is dilated to a segment with endpoints (0, 6) and (−4.5,0) . what is the scale factor of the dilation? enter the correct answer in the ? enter the correct answer in the box.

Answer 1

The scale factor of the dilation from a segment with endpoints (0,8) and (-6,0) to a segment with endpoints (0,6) and (-4.5,0) is 0.75.

Step-by-step explanation:

The scale factor of the dilation in question can be determined by comparing the lengths of the corresponding segments before and after the dilation. The original segment has endpoints at (0,8) and (-6,0), and the dilated segment has endpoints at (0,6) and (-4.5,0). To find the scale factor, we compare the corresponding lengths of the segments in each dimension.

In the y-dimension, the original segment's length is 8 (from 0 to 8), and the dilated segment's length is 6 (from 0 to 6). Therefore, the scale factor in the y-dimension is 6/8, which simplifies to 3/4 or 0.75.

In the x-dimension, the original segment's length is 6 (from 0 to -6), and the dilated segment's length is 4.5 (from 0 to -4.5). The scale factor in this case is also 4.5/6, which simplifies to 3/4 or 0.75.

Since the scale factor is consistent in both x and y dimensions, we conclude that the scale factor of the dilation is 0.75.