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Points A, B, and C are on line segment m. Point B is the midpoint of the segment and A and C are the endpoints. If BC = 4x and AC = x -9 what is the length of AB ? A 4. 36 D 72 O O

Points A, B, and C are on line segment m. Point B is the midpoint of the segment and A and C are the endpoints. If BC = 4x and AC = x -9 what is the length of AB ? A 4. 36 D 72 O O

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Question 14** Points A, B, and C are on line segment \( m \). Point B is the midpoint of the segment, and A and C are the endpoints. If \( BC = 4x \) and \( AC = x^2 - 9 \), what is the length of \( \overline{AB} \)? - A. 4 - B. 9 - C. 36 - D. 72 **Explanation**: Since point B is the midpoint, the length of \( \overline{AB} \) is equal to the length of \( \overline{BC} \). We have: 1. \( BC = 4x \) 2. \( AC = x^2 - 9 \) Given that B is the midpoint, we have: \[ AB = BC = \frac{AC}{2} \] Use this relation to solve for \( AB \).
Transcribed Image Text:**Question 14** Points A, B, and C are on line segment \( m \). Point B is the midpoint of the segment, and A and C are the endpoints. If \( BC = 4x \) and \( AC = x^2 - 9 \), what is the length of \( \overline{AB} \)? - A. 4 - B. 9 - C. 36 - D. 72 **Explanation**: Since point B is the midpoint, the length of \( \overline{AB} \) is equal to the length of \( \overline{BC} \). We have: 1. \( BC = 4x \) 2. \( AC = x^2 - 9 \) Given that B is the midpoint, we have: \[ AB = BC = \frac{AC}{2} \] Use this relation to solve for \( AB \).
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