CONSTRUCT ARGUMENTS Mariah is training for a sprint- distance triathlon. She plans on cycling from her house to the library, shown on the grid with a scale in miles. If the cycling portion of the triathlon is 12 miles, will Mariah have cycled at least of that distance during her bike ride? Justify your argument. Library (4, 9) Mariah's house (9, 2) Clear
CONSTRUCT ARGUMENTS Mariah is training for a sprint- distance triathlon. She plans on cycling from her house to the library, shown on the grid with a scale in miles. If the cycling portion of the triathlon is 12 miles, will Mariah have cycled at least of that distance during her bike ride? Justify your argument. Library (4, 9) Mariah's house (9, 2) Clear
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
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![**Construct Arguments**
Mariah is training for a sprint-distance triathlon. She plans on cycling from her house to the library, shown on the grid with a scale in miles. If the cycling portion of the triathlon is 12 miles, will Mariah have cycled at least \( \frac{2}{3} \) of that distance during her bike ride? Justify your argument.
**Diagram Explanation:**
The grid represents a map with each square corresponding to 1 mile. The diagram shows Mariah's house at coordinates (9, 2) and the library at coordinates (4, 9). To determine the distance Mariah will cycle, we calculate the distance between these two points using the grid.
**Distance Calculation:**
Using the grid points:
- Horizontal distance: \( 9 - 4 = 5 \) miles
- Vertical distance: \( 9 - 2 = 7 \) miles
The total distance Mariah will cycle is the sum of these distances:
\[ 5 + 7 = 12 \] miles
**Comparison with Triathlon Requirement:**
The required distance is \( \frac{2}{3} \) of 12 miles:
\[ \frac{2}{3} \times 12 = 8 \] miles
Mariah will cycle 12 miles, which is more than 8 miles. Thus, she will have cycled at least \( \frac{2}{3} \) of the triathlon distance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4dd8a362-8ff7-49c5-8438-dcaa347410d0%2F8cc185c7-20ec-4307-a155-9c46c99a4ae9%2Fq577lz_processed.png&w=3840&q=75)
Transcribed Image Text:**Construct Arguments**
Mariah is training for a sprint-distance triathlon. She plans on cycling from her house to the library, shown on the grid with a scale in miles. If the cycling portion of the triathlon is 12 miles, will Mariah have cycled at least \( \frac{2}{3} \) of that distance during her bike ride? Justify your argument.
**Diagram Explanation:**
The grid represents a map with each square corresponding to 1 mile. The diagram shows Mariah's house at coordinates (9, 2) and the library at coordinates (4, 9). To determine the distance Mariah will cycle, we calculate the distance between these two points using the grid.
**Distance Calculation:**
Using the grid points:
- Horizontal distance: \( 9 - 4 = 5 \) miles
- Vertical distance: \( 9 - 2 = 7 \) miles
The total distance Mariah will cycle is the sum of these distances:
\[ 5 + 7 = 12 \] miles
**Comparison with Triathlon Requirement:**
The required distance is \( \frac{2}{3} \) of 12 miles:
\[ \frac{2}{3} \times 12 = 8 \] miles
Mariah will cycle 12 miles, which is more than 8 miles. Thus, she will have cycled at least \( \frac{2}{3} \) of the triathlon distance.
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