Question

the image of δabc after a reflection across $overleftrightarrow{eg}$ is δabc. which statement is true about point f? f is the midpoint of $overline{aa}$ because $overleftrightarrow{eg}$ bisects $overline{aa}$. f is the midpoint of $overline{eg}$ because $overline{aa}$ bisects $overline{eg}$. f is the midpoint of $overline{aa}$ because $overline{aa}$ bisects $overline{eg}$. f is the midpoint of $overline{eg}$ because $overleftrightarrow{eg}$ bisects $overline{aa}$.

Explanation:

When a figure is reflected over a line (here, \(\overleftrightarrow{EG}\)), the line of reflection is the perpendicular bisector of the segment joining a point and its image (e.g., \(A\) and \(A'\)). So, \(\overleftrightarrow{EG}\) bisects \(\overline{AA'}\), meaning the intersection point \(F\) of \(\overline{AA'}\) and \(\overleftrightarrow{EG}\) is the midpoint of \(\overline{AA'}\) because \(\overleftrightarrow{EG}\) bisects \(\overline{AA'}\).

Answer:

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