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
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
Related questions
Question
![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 \((7, 2)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4629049e-776a-488c-a468-69a57e6338b6%2F73d0dd71-9cc4-4cca-a731-30308b0085ec%2F6xal37_processed.jpeg&w=3840&q=75)
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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