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 aa bisects eg. f is the mid - point of aa because aa bisects eg. f is the mid - point of eg because eg bisects aa.

Explanation:

Step1: Recall reflection property

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

Step2: Identify mid - point

If a line bisects a line segment, the point of intersection of the line and the segment is the mid - point of the segment. Since $\overleftrightarrow{EG}$ bisects $\overline{AA'}$ and they intersect at point $F$, $F$ is the mid - point of $\overline{AA'}$.

Answer:

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