A map of three public schools was created using a coordinate plane where the origin represents the center of the town. Euclid Elem

Question

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)

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1 month 2022-12-24T17:09:10+00:00 1 Answer 0 views 0

Part A: 7 miles
Part B: 5 miles
Part C: √74 or 8.60 miles
Part D: Braylen went the shortest distance
Step-by-step explanation:
Part A:
EE: (-4, 3); MM: (3, 3)
(x₁, y₁)         (x₂, y₂)
d = √(x₂ – x₁)² + (y₂ – y₁)²
d = √(3 – (-4))² + (3 – 3)²
d = √(7)² + (0)²
d = √49
d = 7 miles
Part B:
EE: (-4, 3); HH: (-4, -2)
(x₁, y₁)         (x₂, y₂)
d = √(x₂ – x₁)² + (y₂ – y₁)²
d = √(-4 – (-4)² + (-2 – 3)²
d = √(0)² + (-5)²
d = √25
d = 5 miles
Part C:
MM: (3, 3); HH: (-4, -2)
(x₁, y₁)         (x₂, y₂)
d = √(x₂ – x₁)² + (y₂ – y₁)²
d = √(-4 – 3)² + (-2 – 3)²
d = √(-7)² + (-5)²
d = √49 + 25
d = √74 or 8.60 miles
Part D:
Javi: HH: (-4, -2); EE: (-4, 3); MM: (3, 3)

HH: (-4, -2); EE: (-4, 3);
(x₁, y₁)         (x₂, y₂)
d = √(x₂ – x₁)² + (y₂ – y₁)²
d = √(-4 – (-4))² + (3 – (-2))²
d = √(0)² + (5)²
d = √25
d = 5 miles
EE: (-4, 3); MM: (3, 3)
(x₁, y₁)         (x₂, y₂)
d = √(x₂ – x₁)² + (y₂ – y₁)²
d = √(3 – (-4))² + (3 – 3)²
d = √(7)² + (0)²
d = √49
d = 7 miles
5 + 7 = 12 miles
——————————————————-
Braylen: HH: (-4, -2); MM: (3, 3)
(x₁, y₁)         (x₂, y₂)
d = √(x₂ – x₁)² + (y₂ – y₁)²
d = √(3 – (-4))² + (3 – (-2))²
d = √(7)² + (5)²
d = √49 + 25
d = √74 or 8.60 miles
Braylen went the shortest distance.