Reyna's house is 12 blocks due west of school. Shaquille's house is 9 blocks due north of the school. Shaquille walks to Reyna's house every morning and then they walk to school together. What is the shortest distance Shaquille could walk on his way to school when he walks with Reyna? O 15 blocks O 27 blocks O 21 blocks O 24 blocks Reyna's house Shaquille's house School Drawing not to scale Submit Answer
Reyna's house is 12 blocks due west of school. Shaquille's house is 9 blocks due north of the school. Shaquille walks to Reyna's house every morning and then they walk to school together. What is the shortest distance Shaquille could walk on his way to school when he walks with Reyna? O 15 blocks O 27 blocks O 21 blocks O 24 blocks Reyna's house Shaquille's house School Drawing not to scale Submit Answer
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter3: Graphing Linear Functions
Section3.1: Functions
Problem 44E
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![**Mathematics Educational Resource**
**Problem Description:**
Reyna's house is 12 blocks due west of school. Shaquille's house is 9 blocks due north of the school. Shaquille walks to Reyna's house every morning and then they walk to school together. What is the shortest distance Shaquille could walk on his way to school when he walks with Reyna?
**Answer Options:**
- 15 blocks
- 21 blocks
- 27 blocks
- 24 blocks
**Diagram Explanation:**
The diagram shows three points representing the locations:
- Shaquille's house (top right).
- Reyna's house (bottom left).
- School (bottom right).
The houses and school are connected by lines representing the distances:
- A vertical line from the school to Shaquille's house (9 blocks).
- A horizontal line from the school to Reyna's house (12 blocks).
- A diagonal dashed line indicating the path Shaquille could walk from his house to Reyna's house and then to the school.
**Solution Approach:**
To determine the shortest distance Shaquille could walk to the school via Reyna's house, use the Pythagorean theorem for the right triangle formed by the straight paths:
\[
a^2 + b^2 = c^2
\]
where \(a = 9\) blocks (north) and \(b = 12\) blocks (west).
Calculate:
\[
c = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15 \text{ blocks}
\]
Thus, the shortest distance Shaquille could walk on his way to school when he walks with Reyna is:
**15 blocks**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0890c2ce-3692-4718-a578-4f9466fde9bf%2F96f538dc-7e91-443f-98fd-8d9ebdfb9588%2F50qqeub_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Mathematics Educational Resource**
**Problem Description:**
Reyna's house is 12 blocks due west of school. Shaquille's house is 9 blocks due north of the school. Shaquille walks to Reyna's house every morning and then they walk to school together. What is the shortest distance Shaquille could walk on his way to school when he walks with Reyna?
**Answer Options:**
- 15 blocks
- 21 blocks
- 27 blocks
- 24 blocks
**Diagram Explanation:**
The diagram shows three points representing the locations:
- Shaquille's house (top right).
- Reyna's house (bottom left).
- School (bottom right).
The houses and school are connected by lines representing the distances:
- A vertical line from the school to Shaquille's house (9 blocks).
- A horizontal line from the school to Reyna's house (12 blocks).
- A diagonal dashed line indicating the path Shaquille could walk from his house to Reyna's house and then to the school.
**Solution Approach:**
To determine the shortest distance Shaquille could walk to the school via Reyna's house, use the Pythagorean theorem for the right triangle formed by the straight paths:
\[
a^2 + b^2 = c^2
\]
where \(a = 9\) blocks (north) and \(b = 12\) blocks (west).
Calculate:
\[
c = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15 \text{ blocks}
\]
Thus, the shortest distance Shaquille could walk on his way to school when he walks with Reyna is:
**15 blocks**.
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