Question

in the figure shown, $overleftrightarrow{gl}$ and $overleftrightarrow{jl}$ intersect at point $l$, and point $m$ is not on either line. both lines will be dilated using a scale factor of 2 and the same center of dilation. which point should be used as the center of dilation so that neither image results in the same line as its preimage? a. point $g$ b. point $j$ c. point $l$ d. point $m$

Explanation:

Step1: Recall dilation properties

If the center of dilation is on a line, the line and its image after dilation are the same when the scale - factor is non - zero.

Step2: Analyze each point

• If the center of dilation is point $G$, line $\overleftrightarrow{GL}$ will be the same line as its pre - image because $G$ lies on $\overleftrightarrow{GL}$.
• If the center of dilation is point $J$, line $\overleftrightarrow{JL}$ will be the same line as its pre - image because $J$ lies on $\overleftrightarrow{JL}$.
• If the center of dilation is point $L$, both $\overleftrightarrow{GL}$ and $\overleftrightarrow{JL}$ will be the same lines as their pre - images since $L$ is the intersection point of the two lines and lies on both lines.
• If the center of dilation is point $M$ (which is not on either line $\overleftrightarrow{GL}$ or $\overleftrightarrow{JL}$), when we dilate the two lines with a scale factor of 2, neither image will be the same line as its pre - image.

Answer:

D. point $M$