Question

select the correct answer
$overline{jk}$ is dilated by a scale factor of $n$ with the origin as the center of dilation, resulting in the image $overline{jk}$. the slope of $overline{jk}$ is $m$. if the length of $overline{jk}$ is $l$, what is the length of $overline{jk}$?
a. $m\times n\times l$
b. $(m + n)\times l$
c. $m\times l$
d. $n\times l$

Explanation:

Step1: Recall the property of dilation

Dilation changes the length of a segment. The formula for the length of the image of a segment after dilation is \( \text{Length of image}=\text{Scale factor}\times\text{Length of original segment}\).

Step2: Apply the formula

Given the scale factor \(n\) and the length of the original segment \(\overline{JK}\) is \(l\). Using the formula \( \text{Length of }\overline{J'K'}=n\times l\)

Answer:

D. \(n\times l\)