Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter9: Real Numbers And Right Triangles
Section9.5: The Distance And Midpoint Formulas
Problem 2C
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### Question 3:
**Problem Statement:**
The diameter of a circle has endpoints at \( (11, 7) \) and \( (-13, 3) \). What are the coordinates of the center of the circle?
---
**Solution Explanation:**
To find the center of the circle, we need to find the midpoint of the line segment with endpoints at \( (11, 7) \) and \( (-13, 3) \). The formula for the midpoint, \( M \), of a line segment with endpoints \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Plugging in the given coordinates:
\[
\begin{align*}
x_1 &= 11, & y_1 &= 7 \\
x_2 &= -13, & y_2 &= 3
\end{align*}
\]
**Coordinates Calculation:**
\[
\begin{align*}
M_x &= \frac{11 + (-13)}{2} = \frac{11 - 13}{2} = \frac{-2}{2} = -1, \\
M_y &= \frac{7 + 3}{2} = \frac{10}{2} = 5
\end{align*}
\]
Thus, the coordinates of the center of the circle are \( (-1, 5) \).
### Answer:
The coordinates of the center of the circle are \( (-1, 5) \).
---
**Graph Explanation:**
There is a blank rectangular placeholder in the lower part of the image. This space can be utilized for any additional diagrams or graphs to visually illustrate the solution, such as a diagram showing the circle and its diameter with marked endpoints and the center.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb79fdde3-ca8a-49c1-94d4-58707404c7a1%2Fed845321-3461-4404-a200-7f3d0ae787d9%2F09b1j0a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Question 3:
**Problem Statement:**
The diameter of a circle has endpoints at \( (11, 7) \) and \( (-13, 3) \). What are the coordinates of the center of the circle?
---
**Solution Explanation:**
To find the center of the circle, we need to find the midpoint of the line segment with endpoints at \( (11, 7) \) and \( (-13, 3) \). The formula for the midpoint, \( M \), of a line segment with endpoints \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Plugging in the given coordinates:
\[
\begin{align*}
x_1 &= 11, & y_1 &= 7 \\
x_2 &= -13, & y_2 &= 3
\end{align*}
\]
**Coordinates Calculation:**
\[
\begin{align*}
M_x &= \frac{11 + (-13)}{2} = \frac{11 - 13}{2} = \frac{-2}{2} = -1, \\
M_y &= \frac{7 + 3}{2} = \frac{10}{2} = 5
\end{align*}
\]
Thus, the coordinates of the center of the circle are \( (-1, 5) \).
### Answer:
The coordinates of the center of the circle are \( (-1, 5) \).
---
**Graph Explanation:**
There is a blank rectangular placeholder in the lower part of the image. This space can be utilized for any additional diagrams or graphs to visually illustrate the solution, such as a diagram showing the circle and its diameter with marked endpoints and the center.
---
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