A map of three public schools was created using a coordinate plane where the origin represents the center of the town. Euclid Elementary School is graphed at (−3, 5), Math Middle School is graphed at (5, 5), and Hypotenuse High School is graphed at (−3, −2). Each unit on the graph represents 1 mile.

Part A: Find the shortest distance, in miles, from Euclid Elementary School to Math Middle School. Show every step of your work. (2 points)

Part B: Find the shortest distance, in miles, from Euclid Elementary School to Hypotenuse High School. Show every step of your work. (2 points)

Part C: Find the shortest distance, in miles, from Math Middle School to Hypotenuse High School. Show every step of your work. (4 points)

Part D: Javi traveled from Hypotenuse High to Euclid Elementary and then to Math Middle. Braylen traveled from Hypotenuse High to Math Middle along a straight path. Who went the shortest distance? Explain. (4 points)

1 answer

Part A:
Distance from Euclid Elementary School to Math Middle School:
Using the distance formula:
√[ (5 - (-3))^2 + (5 - 5)^2 ]
= √[ 8^2 + 0^2 ]
= √64
= 8 miles

Part B:
Distance from Euclid Elementary School to Hypotenuse High School:
Using the distance formula:
√[ (-2 - 5)^2 + (-3 - (-3))^2 ]
= √[ (-7)^2 + 0^2 ]
= √49
= 7 miles

Part C:
Distance from Math Middle School to Hypotenuse High School:
Using the distance formula:
√[ (-2 - 5)^2 + (5 - (-3))^2 ]
= √[ (-7)^2 + 8^2 ]
= √[ 49 + 64 ]
= √113
≈ 10.63 miles

Part D:
Javi's total distance traveled:
Hypotenuse High to Euclid Elementary: 7 miles
Euclid Elementary to Math Middle: 8 miles
Total = 7 + 8 = 15 miles

Braylen's distance traveled:
Hypotenuse High to Math Middle: 10.63 miles

Therefore, Braylen traveled the shortest distance of approximately 10.63 miles.