Which of the following are true of AB given A(9, 5) and B(15, 2)? Select all that apply. A. The midpoint is (12, 3.5). В. The slope of the perpendicular bisector is C. The slope of the perpendicular bisector is 2. D. The slope of the segment is E. The distances from the endpoints of the segment to any point on the perpendicular bisector are equal.

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
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Question26 j11

### Geometry Problem on Perpendicular Bisector and Midpoint

#### Problem Statement:
Given the points \( A(9, 5) \) and \( B(15, 2) \), which of the following statements are true about line segment \( \overline{AB} \)? Select all that apply.

#### Options:

- **A.** The midpoint is \( (12, 3.5) \).
- **B.** The slope of the perpendicular bisector is \( -\frac{1}{2} \).
- **C.** The slope of the perpendicular bisector is \( 2 \).
- **D.** The slope of the segment is \( -\frac{1}{2} \).
- **E.** The distances from the endpoints of the segment to any point on the perpendicular bisector are equal.

#### Explanation:
- **Option A** involves calculating the midpoint of the segment \( \overline{AB} \).
- **Options B and C** discuss the slope of the perpendicular bisector.
- **Option D** pertains to the slope of the segment \( \overline{AB} \).
- **Option E** refers to the geometric property of a perpendicular bisector.

This task tests understanding of the slope of lines, calculation of midpoints, and properties of perpendicular bisectors in the coordinate plane.
Transcribed Image Text:### Geometry Problem on Perpendicular Bisector and Midpoint #### Problem Statement: Given the points \( A(9, 5) \) and \( B(15, 2) \), which of the following statements are true about line segment \( \overline{AB} \)? Select all that apply. #### Options: - **A.** The midpoint is \( (12, 3.5) \). - **B.** The slope of the perpendicular bisector is \( -\frac{1}{2} \). - **C.** The slope of the perpendicular bisector is \( 2 \). - **D.** The slope of the segment is \( -\frac{1}{2} \). - **E.** The distances from the endpoints of the segment to any point on the perpendicular bisector are equal. #### Explanation: - **Option A** involves calculating the midpoint of the segment \( \overline{AB} \). - **Options B and C** discuss the slope of the perpendicular bisector. - **Option D** pertains to the slope of the segment \( \overline{AB} \). - **Option E** refers to the geometric property of a perpendicular bisector. This task tests understanding of the slope of lines, calculation of midpoints, and properties of perpendicular bisectors in the coordinate plane.
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