Question

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?

Answer 1

3750 ft

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:

• 
  `AB=√((-2-(-2))^2+(1-(-7))^2)=8\ units;`
• 
  `BC=√((-2-5)^2+(-7-(-7))^2)=7\ units;`
• 
  `CD=√((5-5)^2+(1-(-7))^2)=8\ units;`
• 
  `DA=√((5-(-2))^2+(1-1)^2)=7\ units.`

The total distance Paolo walked is

`8+7+8+7=30\ units.`

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

`30\cdot 125=3750\ ft.`