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В X+1 X +7 Let AC = 16, AB = x + 1, and BC = x + 7. What is the measure of the length of AB? 4 O5 O 1 O 16

В X+1 X +7 Let AC = 16, AB = x + 1, and BC = x + 7. What is the measure of the length of AB? 4 O5 O 1 O 16

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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### Problem Statement: Given three points \(A\), \(B\), and \(C\) on a line segment, we know the following: - \(AC = 16\) - \(AB = x + 1\) - \(BC = x + 7\) The problem is to determine the measure of the length of \( \overline{AB} \). ### Diagram: The diagram shows a straight line segment with: - Point \(A\) at the left end. - Point \(B\) somewhere between points \(A\) and \(C\) (closer to \(A\)). - Point \(C\) at the right end. Below is the diagram: \[ A \quad \quad \quad \quad B \quad \quad \quad \quad C \] \[ \bullet \quad \quad \quad \bullet \quad \quad \quad \bullet \] \[ \quad x + 1 \quad \quad \quad \quad x + 7 \] ### Equations and Solution: We know from the problem statement that: \[ AB + BC = AC \] Substituting the given lengths: \[ (x + 1) + (x + 7) = 16 \] \[ x + 1 + x + 7 = 16 \] \[ 2x + 8 = 16 \] Subtracting 8 from both sides: \[ 2x = 8 \] Dividing by 2: \[ x = 4 \] Now, substituting \(x = 4\) back into \(AB\): \[ AB = x + 1 = 4 + 1 = 5 \] ### Answer: \[ \boxed{5} \] Multiple choice options: - \(\bullet\) 4 - \( \circ\) 5 - \( \circ\) 11 - \( \circ\) 16 The correct answer is **5**. Thus, the measure of the length of \( \overline{AB} \) is 5 units.
Transcribed Image Text:### Problem Statement: Given three points \(A\), \(B\), and \(C\) on a line segment, we know the following: - \(AC = 16\) - \(AB = x + 1\) - \(BC = x + 7\) The problem is to determine the measure of the length of \( \overline{AB} \). ### Diagram: The diagram shows a straight line segment with: - Point \(A\) at the left end. - Point \(B\) somewhere between points \(A\) and \(C\) (closer to \(A\)). - Point \(C\) at the right end. Below is the diagram: \[ A \quad \quad \quad \quad B \quad \quad \quad \quad C \] \[ \bullet \quad \quad \quad \bullet \quad \quad \quad \bullet \] \[ \quad x + 1 \quad \quad \quad \quad x + 7 \] ### Equations and Solution: We know from the problem statement that: \[ AB + BC = AC \] Substituting the given lengths: \[ (x + 1) + (x + 7) = 16 \] \[ x + 1 + x + 7 = 16 \] \[ 2x + 8 = 16 \] Subtracting 8 from both sides: \[ 2x = 8 \] Dividing by 2: \[ x = 4 \] Now, substituting \(x = 4\) back into \(AB\): \[ AB = x + 1 = 4 + 1 = 5 \] ### Answer: \[ \boxed{5} \] Multiple choice options: - \(\bullet\) 4 - \( \circ\) 5 - \( \circ\) 11 - \( \circ\) 16 The correct answer is **5**. Thus, the measure of the length of \( \overline{AB} \) is 5 units.
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