Use the given endpoint R and midpoint M of RS to find the coordinates of the other endpoint S. 8) R (3, 0), M (0, 5) 9) R (5, 1), M (1, 4) 10) Mr. Franklin needs to draw a perfect circle. The endpoints of one of the diameters needs to fall on (7, 1) and (-1, -1). Where should he locate the center of the circle?
Use the given endpoint R and midpoint M of RS to find the coordinates of the other endpoint S. 8) R (3, 0), M (0, 5) 9) R (5, 1), M (1, 4) 10) Mr. Franklin needs to draw a perfect circle. The endpoints of one of the diameters needs to fall on (7, 1) and (-1, -1). Where should he locate the center of the circle?
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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![### Coordinate Geometry: Using Endpoint and Midpoint
In this task, we are provided with an endpoint \( R \) and the midpoint \( M \) of a line segment \( RS \). We need to find the coordinates of the other endpoint \( S \).
#### Problem Statements
8) Given:
- Endpoint \( R(3, 0) \)
- Midpoint \( M(0, 5) \)
Find the coordinates of the other endpoint \( S \).
9) Given:
- Endpoint \( R(5, 1) \)
- Midpoint \( M(1, 4) \)
Find the coordinates of the other endpoint \( S \).
---
#### Circle Geometry: Finding the Center
10) Mr. Franklin needs to draw a perfect circle. The endpoints of one of the diameters are given as (7, 1) and (-1, -1). Where should he locate the center of the circle?
#### Solution Approach
**For Problems 8 and 9:**
To find the coordinates of the other endpoint, we use the midpoint formula:
\[ M\left(x, y\right) = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \]
Given the coordinates of \( R \left(x_1, y_1\right) \) and \( M \left(x, y\right) \), we can solve for the coordinates of \( S \left(x_2, y_2\right) \).
**For Problem 10:**
The center of the circle, which is the midpoint of the diameter, can be found using the midpoint formula:
\[ \text{Center of the circle} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Using the given endpoints (7, 1) and (-1, -1), substitute these values into the formula to find the center of the circle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc5101586-b16b-4e8c-bc6f-6b8b2323a7d8%2F415f062b-bdb8-4e49-8537-b6f180a6760f%2Fiykfcpo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Coordinate Geometry: Using Endpoint and Midpoint
In this task, we are provided with an endpoint \( R \) and the midpoint \( M \) of a line segment \( RS \). We need to find the coordinates of the other endpoint \( S \).
#### Problem Statements
8) Given:
- Endpoint \( R(3, 0) \)
- Midpoint \( M(0, 5) \)
Find the coordinates of the other endpoint \( S \).
9) Given:
- Endpoint \( R(5, 1) \)
- Midpoint \( M(1, 4) \)
Find the coordinates of the other endpoint \( S \).
---
#### Circle Geometry: Finding the Center
10) Mr. Franklin needs to draw a perfect circle. The endpoints of one of the diameters are given as (7, 1) and (-1, -1). Where should he locate the center of the circle?
#### Solution Approach
**For Problems 8 and 9:**
To find the coordinates of the other endpoint, we use the midpoint formula:
\[ M\left(x, y\right) = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \]
Given the coordinates of \( R \left(x_1, y_1\right) \) and \( M \left(x, y\right) \), we can solve for the coordinates of \( S \left(x_2, y_2\right) \).
**For Problem 10:**
The center of the circle, which is the midpoint of the diameter, can be found using the midpoint formula:
\[ \text{Center of the circle} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Using the given endpoints (7, 1) and (-1, -1), substitute these values into the formula to find the center of the circle.
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