Polygon jklm is dilated by a scale factor of 2.5 with point c as the center of dialation, resulting in the image j'k'l'm'. if point c lies on lm and the slope of lm is 1.75, what can be said about l'm'? a) l'm' has a slope of 1.75 but does not pass through point c. b) l'm' has a slope of 2.5 but does not pass through point c. l'm' has a slope of 1.75 and passes through point c. c) l'm' has a slope of 2.5 but does not pass through point c.

The correct option C.

Step-by-step explanation:

It is given that J'K'L'M' is the image of polygon JKLM after dilation. The scale factor of dilation is 2.5 with center C. Point C lies on LM. Slope of LM is 1.75.

Dilation is the enlargement and compression of a figure. The corresponding sides of image and preimage are proportional.

The slopes of corresponding sides are equal because they are parallel to each other. Therefore the slope of L'M' is 1.75.

If a line passing through the center of the dilation, then the image is  enlargement and compression of the line and image is passing through the center. So, L'M' passing through the center C.

Therefore option C is correct.