### Finding the Midpoint \( M \) of Line Segment \( \overline{CD} \) To find the midpoint \( M \) of the line segment \( \overline{CD} \), we use the midpoint formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Given the coordinates of points \( C \) and \( D \): - \( C = (-2, -10) \) - \( D = (-6, 0) \) Plugging these coordinates into the formula, we have: \[ x_1 = -2, \, y_1 = -10, \, x_2 = -6, \, y_2 = 0 \] #### Calculating Midpoint Coordinates 1. Calculate the x-coordinate of the midpoint: \[ \frac{-2 + (-6)}{2} = \frac{-2 - 6}{2} = \frac{-8}{2} = -4 \] 2. Calculate the y-coordinate of the midpoint: \[ \frac{-10 + 0}{2} = \frac{-10}{2} = -5 \] Thus, the midpoint \( M \) is: \[ M = (-4, -5) \] ### Interactive Question **Instruction**: Enter the number that belongs in the green box. **Interactive Box**: \[ M = \left( [ \green \boxed{-4} ], [ \, ] \right) \] **Input Field**: [ ] **Enter Button**: [Enter] ### Summary The green box should contain the value \( -4 \), which is the x-coordinate of the midpoint \( M \). --- © 2003 - 2021 Acellus Corporation. All Rights Reserved.
### Finding the Midpoint \( M \) of Line Segment \( \overline{CD} \) To find the midpoint \( M \) of the line segment \( \overline{CD} \), we use the midpoint formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Given the coordinates of points \( C \) and \( D \): - \( C = (-2, -10) \) - \( D = (-6, 0) \) Plugging these coordinates into the formula, we have: \[ x_1 = -2, \, y_1 = -10, \, x_2 = -6, \, y_2 = 0 \] #### Calculating Midpoint Coordinates 1. Calculate the x-coordinate of the midpoint: \[ \frac{-2 + (-6)}{2} = \frac{-2 - 6}{2} = \frac{-8}{2} = -4 \] 2. Calculate the y-coordinate of the midpoint: \[ \frac{-10 + 0}{2} = \frac{-10}{2} = -5 \] Thus, the midpoint \( M \) is: \[ M = (-4, -5) \] ### Interactive Question **Instruction**: Enter the number that belongs in the green box. **Interactive Box**: \[ M = \left( [ \green \boxed{-4} ], [ \, ] \right) \] **Input Field**: [ ] **Enter Button**: [Enter] ### Summary The green box should contain the value \( -4 \), which is the x-coordinate of the midpoint \( M \). --- © 2003 - 2021 Acellus Corporation. All Rights Reserved.
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 Midpoint \( M \) of Line Segment \( \overline{CD} \)
To find the midpoint \( M \) of the line segment \( \overline{CD} \), we use the midpoint formula:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Given the coordinates of points \( C \) and \( D \):
- \( C = (-2, -10) \)
- \( D = (-6, 0) \)
Plugging these coordinates into the formula, we have:
\[ x_1 = -2, \, y_1 = -10, \, x_2 = -6, \, y_2 = 0 \]
#### Calculating Midpoint Coordinates
1. Calculate the x-coordinate of the midpoint:
\[ \frac{-2 + (-6)}{2} = \frac{-2 - 6}{2} = \frac{-8}{2} = -4 \]
2. Calculate the y-coordinate of the midpoint:
\[ \frac{-10 + 0}{2} = \frac{-10}{2} = -5 \]
Thus, the midpoint \( M \) is:
\[ M = (-4, -5) \]
### Interactive Question
**Instruction**: Enter the number that belongs in the green box.
**Interactive Box**:
\[ M = \left( [ \green \boxed{-4} ], [ \, ] \right) \]
**Input Field**: [ ]
**Enter Button**: [Enter]
### Summary
The green box should contain the value \( -4 \), which is the x-coordinate of the midpoint \( M \).
---
© 2003 - 2021 Acellus Corporation. All Rights Reserved.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdcc7be8e-76d1-4e42-824d-ffb9dd6ef69a%2F9081ee2f-05a7-4c79-9e22-332e19108eb4%2Ft3fux6.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Midpoint \( M \) of Line Segment \( \overline{CD} \)
To find the midpoint \( M \) of the line segment \( \overline{CD} \), we use the midpoint formula:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Given the coordinates of points \( C \) and \( D \):
- \( C = (-2, -10) \)
- \( D = (-6, 0) \)
Plugging these coordinates into the formula, we have:
\[ x_1 = -2, \, y_1 = -10, \, x_2 = -6, \, y_2 = 0 \]
#### Calculating Midpoint Coordinates
1. Calculate the x-coordinate of the midpoint:
\[ \frac{-2 + (-6)}{2} = \frac{-2 - 6}{2} = \frac{-8}{2} = -4 \]
2. Calculate the y-coordinate of the midpoint:
\[ \frac{-10 + 0}{2} = \frac{-10}{2} = -5 \]
Thus, the midpoint \( M \) is:
\[ M = (-4, -5) \]
### Interactive Question
**Instruction**: Enter the number that belongs in the green box.
**Interactive Box**:
\[ M = \left( [ \green \boxed{-4} ], [ \, ] \right) \]
**Input Field**: [ ]
**Enter Button**: [Enter]
### Summary
The green box should contain the value \( -4 \), which is the x-coordinate of the midpoint \( M \).
---
© 2003 - 2021 Acellus Corporation. All Rights Reserved.
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