Question

the image of △abc after a reflection across eg is △abc. which statement is true about point f? f is the mid - point of aa because eg bisects aa. f is the mid - point of eg because eg bisects aa. f is the mid - point of eg because aa bisects eg. f is the mid - point of aa because aa bisects eg.

Explanation:

Step1: Recall reflection property

In a reflection, the line of reflection bisects the segment joining a point and its image. Here, $\triangle ABC$ is reflected across $\overleftrightarrow{EG}$ to get $\triangle A'B'C'$. So, $\overleftrightarrow{EG}$ bisects $\overline{AA'}$ and the intersection point $F$ of $\overleftrightarrow{EG}$ and $\overline{AA'}$ is the mid - point of $\overline{AA'}$.

Answer:

F is the midpoint of $\overline{AA'}$ because $\overleftrightarrow{EG}$ bisects $\overline{AA'}$.