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)

Respuesta :

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.