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)**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f655a5e-3946-44a0-87d7-d06571787362%2F4a237542-6be4-4c16-a040-934e23bad31c%2Fm6tp33_processed.jpeg&w=3840&q=75)
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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