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The location of four game stops are on a coordinate grid are as follows: Stop 1 at (−2,1) Stop 2 at (−2, −7) ​​ Stop 3 at (5,−7) Stop 4 at (5, 1) Paulo begins at Stop 1 and then walks to Stop 2, then Stop 3, and then Stop 4. Then he walks to Stop 1 again. The path between each stop is a straight line. One unit on the coordinate grid equals 125 feet. What is the total distance Paulo walked?

Respuesta :

frika

Answer:

3750 ft

Step-by-step explanation:

Denote Stops as points A(-2,1), B(-2,-7), C(5,-7) and D(5,1) and find all distances between two consecutive points:

  • [tex]AB=\sqrt{(-2-(-2))^2+(1-(-7))^2}=8\ units;[/tex]
  • [tex]BC=\sqrt{(-2-5)^2+(-7-(-7))^2}=7\ units;[/tex]
  • [tex]CD=\sqrt{(5-5)^2+(1-(-7))^2}=8\ units;[/tex]
  • [tex]DA=\sqrt{(5-(-2))^2+(1-1)^2}=7\ units.[/tex]

The total distance Paolo walked is

[tex]8+7+8+7=30\ units.[/tex]

Since 1 unit on the coordinate grid equals 125 feet, then the total distance Paolo walked is

[tex]30\cdot 125=3750\ ft.[/tex]

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