Questions: Given point A is not on line m, suppose A is reflected across line m. Which of the following is true? A. The line segment AA, is the bisector of line m. B. Line m is the perpendicular bisector of the line segment AA, C. Line m is parallel to the line segment AA, D. A=A′

Given point A is not on line m, suppose A is reflected across line m. Which of the following is true?
A. The line segment AA, is the bisector of line m.
B. Line m is the perpendicular bisector of the line segment AA,
C. Line m is parallel to the line segment AA,
D. A=A′

Transcript text: Given point $A$ is not on line $m$, suppose $A$ is reflected across line $m$. Which of the following is true? A. $\overline{A A}$, is the bisector of line $m$. B. Line $m$ is the perpendicular bisector of $\overline{A A}$, C. Line $m$ is parallel to $\overline{A A}$, D. $A=A^{\prime}$

Solution

The answer is B: Line $ m $ is the perpendicular bisector of $ \overline{A A'} $.

Explanation for each option:

A. $ \overline{A A} $, is the bisector of line $ m $.

This statement is incorrect. A line segment cannot bisect a line. Instead, a line can bisect a line segment.

B. Line $ m $ is the perpendicular bisector of $ \overline{A A'} $.

This statement is correct. When a point $ A $ is reflected across a line $ m $, the line $ m $ acts as the perpendicular bisector of the segment joining the original point $ A $ and its reflection $ A' $. This means that $ m $ is perpendicular to $ \overline{A A'} $ and divides it into two equal parts.

C. Line $ m $ is parallel to $ \overline{A A'} $.

This statement is incorrect. The line $ m $ is not parallel to $ \overline{A A'} $; instead, it is perpendicular to it.

D. $ A = A^{\prime} $

This statement is incorrect. If $ A $ is not on line $ m $, then $ A $ and its reflection $ A' $ are distinct points. They would only be the same if $ A $ were on line $ m $.

In summary, the correct statement is that line $ m $ is the perpendicular bisector of $ \overline{A A'} $.

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