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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![**Finding the Coordinates of B**
**Question:**
The midpoint of \( AB \) is \( M(4, -2) \). If the coordinates of \( A \) are \( (3, -6) \), what are the coordinates of \( B \)?
**Answer:**
**Solution:**
To find the coordinates of \( B \), let's use the midpoint formula. The midpoint \( M \) of a segment with endpoints \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Here, we know:
\( M = (4, -2) \)
\( A = (3, -6) \)
We need to find \( B = (x_2, y_2) \).
From the midpoint formula:
\[ 4 = \frac{3 + x_2}{2} \]
\[ -2 = \frac{-6 + y_2}{2} \]
Let's solve for \( x_2 \) and \( y_2 \):
1. Solve for \( x_2 \):
\[ 4 = \frac{3 + x_2}{2} \]
Multiply both sides by 2:
\[ 8 = 3 + x_2 \]
Subtract 3 from both sides:
\[ x_2 = 5 \]
2. Solve for \( y_2 \):
\[ -2 = \frac{-6 + y_2}{2} \]
Multiply both sides by 2:
\[ -4 = -6 + y_2 \]
Add 6 to both sides:
\[ y_2 = 2 \]
Therefore, the coordinates of \( B \) are \( (5, 2) \).
**Answer Box:**
\[ Answer: (5, 2) \]
**Submit Answer [ ]** (The answer box where you input the coordinates)
*Additional Information:*
- This is the first attempt out of three allowed for this problem.
- The problem is registered as attempt 1 out of max 1.
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Transcribed Image Text:**Finding the Coordinates of B**
**Question:**
The midpoint of \( AB \) is \( M(4, -2) \). If the coordinates of \( A \) are \( (3, -6) \), what are the coordinates of \( B \)?
**Answer:**
**Solution:**
To find the coordinates of \( B \), let's use the midpoint formula. The midpoint \( M \) of a segment with endpoints \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Here, we know:
\( M = (4, -2) \)
\( A = (3, -6) \)
We need to find \( B = (x_2, y_2) \).
From the midpoint formula:
\[ 4 = \frac{3 + x_2}{2} \]
\[ -2 = \frac{-6 + y_2}{2} \]
Let's solve for \( x_2 \) and \( y_2 \):
1. Solve for \( x_2 \):
\[ 4 = \frac{3 + x_2}{2} \]
Multiply both sides by 2:
\[ 8 = 3 + x_2 \]
Subtract 3 from both sides:
\[ x_2 = 5 \]
2. Solve for \( y_2 \):
\[ -2 = \frac{-6 + y_2}{2} \]
Multiply both sides by 2:
\[ -4 = -6 + y_2 \]
Add 6 to both sides:
\[ y_2 = 2 \]
Therefore, the coordinates of \( B \) are \( (5, 2) \).
**Answer Box:**
\[ Answer: (5, 2) \]
**Submit Answer [ ]** (The answer box where you input the coordinates)
*Additional Information:*
- This is the first attempt out of three allowed for this problem.
- The problem is registered as attempt 1 out of max 1.
**Privacy Policy Terms of Service**
- Copyright © 2021 DeltaMath.com. All Rights Reserved.
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