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

Answer ( 1 )

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    2022-12-24T17:10:34+00:00
    Answer:
    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.

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