Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Mathematics Homework Help**
---
**Question 19:** Find the midpoint of the line segment with endpoints \( (7, -4) \) and \( (-5, 8) \).
---
**Explanation:**
To find the midpoint of a line segment with given endpoints, you use the midpoint formula:
\[
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Given the endpoints \( (7, -4) \) and \( (-5, 8) \),
- \( x_1 = 7 \)
- \( y_1 = -4 \)
- \( x_2 = -5 \)
- \( y_2 = 8 \)
Plug these values into the midpoint formula:
\[
= \left( \frac{7 + (-5)}{2}, \frac{-4 + 8}{2} \right)
= \left( \frac{7 - 5}{2}, \frac{-4 + 8}{2} \right)
= \left( \frac{2}{2}, \frac{4}{2} \right)
= (1, 2)
\]
Therefore, the midpoint of the line segment with endpoints \( (7, -4) \) and \( (-5, 8) \) is \( (1, 2) \).
---
**Graphical Representation:**
A graph would show a line segment between the points \( (7, -4) \) and \( (-5, 8) \), with the midpoint marked at \( (1, 2) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18998c65-8b36-476f-a339-d8f4978f3c4a%2F72da4aaa-13ee-4865-9a0b-cb484d1829e0%2F0npr48_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Mathematics Homework Help**
---
**Question 19:** Find the midpoint of the line segment with endpoints \( (7, -4) \) and \( (-5, 8) \).
---
**Explanation:**
To find the midpoint of a line segment with given endpoints, you use the midpoint formula:
\[
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Given the endpoints \( (7, -4) \) and \( (-5, 8) \),
- \( x_1 = 7 \)
- \( y_1 = -4 \)
- \( x_2 = -5 \)
- \( y_2 = 8 \)
Plug these values into the midpoint formula:
\[
= \left( \frac{7 + (-5)}{2}, \frac{-4 + 8}{2} \right)
= \left( \frac{7 - 5}{2}, \frac{-4 + 8}{2} \right)
= \left( \frac{2}{2}, \frac{4}{2} \right)
= (1, 2)
\]
Therefore, the midpoint of the line segment with endpoints \( (7, -4) \) and \( (-5, 8) \) is \( (1, 2) \).
---
**Graphical Representation:**
A graph would show a line segment between the points \( (7, -4) \) and \( (-5, 8) \), with the midpoint marked at \( (1, 2) \).
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