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The coordinate (5, 5) is the midpoint of A and B. If A is located at (3, 8), then what is the location of B? O (2, 7) O (8, 3) O (8, 13) O (7, 2)

The coordinate (5, 5) is the midpoint of A and B. If A is located at (3, 8), then what is the location of B? O (2, 7) O (8, 3) O (8, 13) O (7, 2)

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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The question is as follows: "The coordinate (5, 5) is the midpoint of A and B. If A is located at (3, 8), then what is the location of B?" Options: - (2, 7) - (8, 3) - (8, 13) - (7, 2) Explanation for Educational Context: To find the location of point B, given that (5, 5) is the midpoint between points A and B, and A is at (3, 8), we use the midpoint formula. The midpoint \((M_x, M_y)\) of two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated as: \[ M_x = \frac{x_1 + x_2}{2}, \quad M_y = \frac{y_1 + y_2}{2} \] Given \(M_x = 5\) and \(M_y = 5\), and knowing \(x_1 = 3\) and \(y_1 = 8\) for point A, solve for \(x_2\) and \(y_2\): \[ 5 = \frac{3 + x_2}{2} \quad \Rightarrow \quad 10 = 3 + x_2 \quad \Rightarrow \quad x_2 = 7 \] \[ 5 = \frac{8 + y_2}{2} \quad \Rightarrow \quad 10 = 8 + y_2 \quad \Rightarrow \quad y_2 = 2 \] Thus, the location of B is \((7, 2)\).
Transcribed Image Text:The question is as follows: "The coordinate (5, 5) is the midpoint of A and B. If A is located at (3, 8), then what is the location of B?" Options: - (2, 7) - (8, 3) - (8, 13) - (7, 2) Explanation for Educational Context: To find the location of point B, given that (5, 5) is the midpoint between points A and B, and A is at (3, 8), we use the midpoint formula. The midpoint \((M_x, M_y)\) of two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated as: \[ M_x = \frac{x_1 + x_2}{2}, \quad M_y = \frac{y_1 + y_2}{2} \] Given \(M_x = 5\) and \(M_y = 5\), and knowing \(x_1 = 3\) and \(y_1 = 8\) for point A, solve for \(x_2\) and \(y_2\): \[ 5 = \frac{3 + x_2}{2} \quad \Rightarrow \quad 10 = 3 + x_2 \quad \Rightarrow \quad x_2 = 7 \] \[ 5 = \frac{8 + y_2}{2} \quad \Rightarrow \quad 10 = 8 + y_2 \quad \Rightarrow \quad y_2 = 2 \] Thus, the location of B is \((7, 2)\).
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