Question

polygon jklm is dilated by a scale factor of 2.5 with point c as the center of dilation, resulting in the image jklm. if point c lies on \\(\overline{lm}\\) and the slope of \\(\overline{lm}\\) is 1.75, what can be said about \\(\overline{lm}\\)?

\\(\bigcirc\\) a. \\(\overline{lm}\\) has a slope of 1.75 but does not pass through point c.

\\(\bigcirc\\) b. \\(\overline{lm}\\) has a slope of 2.5 but does not pass through point c.

\\(\bigcirc\\) c. \\(\overline{lm}\\) has a slope of 1.75 and passes through point c.

\\(\bigcirc\\) d. \\(\overline{lm}\\) has a slope of 2.5 and passes through point c.

Explanation:

Step1: Analyze slope after dilation

Dilation preserves slope. Slope of $\overline{LM}$ is 1.75, so slope of $\overline{L'M'}$ is 1.75.

Step2: Check if $\overline{L'M'}$ passes through C

C is on $\overline{LM}$. Dilation centers map to themselves, and dilated points lie on lines from C to original points. Thus, $\overline{L'M'}$ passes through C.

Answer:

C. $\overline{L'M'}$ has a slope of 1.75 and passes through point C.