Question

Building 1(-5,-3) Building 2 is at (- 5, 5) Building 3 is at (4, 5) Building 4 is at (4, - 3) A bike courier begins at building 1 and then delivers packages to building 2 and then building 3, and then building 4. Then she bikes back to building 1. The path between each building is a straight line. One unit on the coordinate grid equals 100 feet What is the total distance the courier biked?

Answer 1

We have to use the distace between points formula to calculate the distance on each case.

Case 1: From Building 1 (-5,-3) to building 2 (-5,5)

`d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}`
`d=\sqrt[]{(-5-(-5))^2+(5-(-3)^2}\text{ = 8}`

Case 2: From Building 2 (-5,5) to building 3 (4, 5)

`d=\sqrt[]{(5-5)^2+(4-(-5))^2}\text{ = }9`

Case 3: From Building 3 (4, 5) to building 4 (4, - 3)

`d=\sqrt[]{(-3-5)^2+(4-4)^2}\text{ = }8`

Case 4: From Building 4 (4, - 3) to building 1 (-5,-3)

`d=\sqrt[]{(-3-(-3))^2+(-5-4)^2}\text{ = }9`

The sum of the distances is: 8+9+8+9= 34. And since one unit equals 100 feet. Then the distance biked is 3400 feet.