What is the midpoint of a segment whose endpointd are (6, 4) and (9, -2)? Answers A -D (7.5, 1) B (7, 2) C (12, 10) D (12,-8)

Intermediate Algebra
19th Edition
ISBN:9780998625720
Author:Lynn Marecek
Publisher:Lynn Marecek
Chapter11: Conics
Section11.1: Distance And Midpoint Formulas; Circles
Problem 11.7TI: Use the Midpoint Formula to find the midpoint of the line segments whose endpoints are (3,5) and...
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### Midpoint Calculation Question

**Question:**
What is the midpoint of a segment whose endpoints are (6, 4) and (9, -2)?

**Answer Choices:**
- A. (7.5, 1)
- B. (7, 2)
- C. (12, 10)
- D. (12, -8)

**Instructions:**
To find the midpoint of a segment, use the midpoint formula, which is:
\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the endpoints of the segment. Plug in the given endpoints (6, 4) and (9, -2) into the formula to find the correct midpoint.

**Solution:**
\[ 
\text{Midpoint} = \left( \frac{6 + 9}{2}, \frac{4 + (-2)}{2} \right) 
= \left( \frac{15}{2}, \frac{2}{2} \right) 
= \left( 7.5, 1 \right) 
\]
Therefore, the correct answer is **A. (7.5, 1)**.
Transcribed Image Text:### Midpoint Calculation Question **Question:** What is the midpoint of a segment whose endpoints are (6, 4) and (9, -2)? **Answer Choices:** - A. (7.5, 1) - B. (7, 2) - C. (12, 10) - D. (12, -8) **Instructions:** To find the midpoint of a segment, use the midpoint formula, which is: \[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the endpoints of the segment. Plug in the given endpoints (6, 4) and (9, -2) into the formula to find the correct midpoint. **Solution:** \[ \text{Midpoint} = \left( \frac{6 + 9}{2}, \frac{4 + (-2)}{2} \right) = \left( \frac{15}{2}, \frac{2}{2} \right) = \left( 7.5, 1 \right) \] Therefore, the correct answer is **A. (7.5, 1)**.
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