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
Related questions
Question
![### Midpoint and Distance Formula Lesson
The endpoints of \( \overline{AB} \) are \( A (0, -4) \) and \( B (4, 2) \). Find the coordinates of the midpoint.
- \( (4, -2) \)
- \( (2, 1) \)
- \( (4, 2) \)
- \( (2, -1) \)
---
**Understanding the Problem:**
To find the midpoint of a line segment given the endpoints, you use the Midpoint Formula. The formula is:
\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the endpoints.
**Calculation:**
Let \( A (0, -4) \) and \( B (4, 2) \).
Plug these coordinates into the Midpoint Formula:
\[ \text{Midpoint} = \left( \frac{0 + 4}{2}, \frac{-4 + 2}{2} \right) \]
\[ \text{Midpoint} = \left( \frac{4}{2}, \frac{-2}{2} \right) \]
\[ \text{Midpoint} = (2, -1) \]
So, the correct answer is:
- \( (2, -1) \)
---
**Question Projection:**
This question is part of an exercise designed to help students understand and apply the Midpoint Formula. The process involves substituting the given coordinates into the formula and simplifying the resulting expressions to find the midpoint of a segment.
By practicing this, students will gain confidence in solving similar problems and be prepared for more complex scenarios involving the concepts of midpoints and distances in a coordinate plane.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0449a0b2-b573-4c37-a73f-7ccfb17fc319%2Fb620c783-27ef-4b38-804c-c5ea3c01ec34%2Frfdvd1h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Midpoint and Distance Formula Lesson
The endpoints of \( \overline{AB} \) are \( A (0, -4) \) and \( B (4, 2) \). Find the coordinates of the midpoint.
- \( (4, -2) \)
- \( (2, 1) \)
- \( (4, 2) \)
- \( (2, -1) \)
---
**Understanding the Problem:**
To find the midpoint of a line segment given the endpoints, you use the Midpoint Formula. The formula is:
\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the endpoints.
**Calculation:**
Let \( A (0, -4) \) and \( B (4, 2) \).
Plug these coordinates into the Midpoint Formula:
\[ \text{Midpoint} = \left( \frac{0 + 4}{2}, \frac{-4 + 2}{2} \right) \]
\[ \text{Midpoint} = \left( \frac{4}{2}, \frac{-2}{2} \right) \]
\[ \text{Midpoint} = (2, -1) \]
So, the correct answer is:
- \( (2, -1) \)
---
**Question Projection:**
This question is part of an exercise designed to help students understand and apply the Midpoint Formula. The process involves substituting the given coordinates into the formula and simplifying the resulting expressions to find the midpoint of a segment.
By practicing this, students will gain confidence in solving similar problems and be prepared for more complex scenarios involving the concepts of midpoints and distances in a coordinate plane.
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