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'

The answer is the second one (B): Line \( m \) is the perpendicular bisector of \(\overline{A A^{\prime}}\).

Explanation for each option:

A. \(\overline{A A^{\prime}}\) is the bisector of line \( m \).

• This is incorrect because \(\overline{A A^{\prime}}\) is not necessarily a bisector of line \( m \). Instead, line \( m \) bisects the segment \(\overline{A A^{\prime}}\).

B. Line \( m \) is the perpendicular bisector of \(\overline{A A^{\prime}}\).

• This 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 reflected image \( A^{\prime} \).

C. Line \( m \) is parallel to \(\overline{A A^{\prime}}\).

• This is incorrect because line \( m \) is perpendicular to \(\overline{A A^{\prime}}\), not parallel.

D. \( A = A^{\prime} \)

• This is incorrect because \( A \) and \( A^{\prime} \) are distinct points unless \( A \) lies on line \( m \), which contradicts the given condition that \( A \) is not on line \( m \).

Summary: The correct statement is that line \( m \) is the perpendicular bisector of \(\overline{A A^{\prime}}\).