Question

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

Explanation:

Step1: Recall reflection property

In a reflection, the line of reflection is the perpendicular - bisector of the line 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: Analyze the position of point F

Since $\overleftrightarrow{EG}$ is the perpendicular - bisector of $\overline{AA'}$, the point of intersection of $\overline{AA'}$ and $\overleftrightarrow{EG}$ (which is point F) is the mid - point of $\overline{AA'}$ because a perpendicular bisector of a line segment divides the line segment into two equal parts.

Answer:

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