Question

which figure shows that $overrightarrow{de}$ is a perpendicular bisector of $overline{ac}$? a. image of option a with points a, b, c, d, e b. image of option b with points a, b, c, d, e c. image of option c with points b, c, d d. image of option d with points a, b, c, d, e

Explanation:

Step1: Recall definition of perpendicular bisector

A perpendicular bisector of a line - segment divides the line - segment into two equal parts and is perpendicular to it. We need to look for a figure where $\overline{DE}$ intersects $\overline{AC}$ at a right - angle and bisects $\overline{AC}$.

Step2: Analyze option A

In option A, $\overline{DE}$ intersects $\overline{AC}$, but there is no indication of right - angle or bisection.

Step3: Analyze option B

In option B, $\overline{DE}$ is perpendicular to $\overline{AC}$, but there is no indication that it bisects $\overline{AC}$.

Step4: Analyze option C

In option C, $\overline{DE}$ is perpendicular to $\overline{AC}$, but there is no indication that it bisects $\overline{AC}$.

Step5: Analyze option D

In option D, $\overline{DE}$ intersects $\overline{AC}$ at a right - angle (shown by the right - angle symbol) and the equal - length marks on $\overline{AB}$ and $\overline{BC}$ indicate that $\overline{DE}$ bisects $\overline{AC}$.

Answer:

D.