Question

Kim drove from Mathtown at (-2, 5) to Geometryville at (3, -1) to Algebra Springs at (-6, -5), and then back to Mathtown. Find the total distance Kim traveled to the nearest hundredth.

Answer 1

Option (3)

Explanation:

To solve this question we will use the formula,

Distance (d) between two points
`(x_1,y_1)` and
`(x_2,y_2)`,

d =
`√((x_2-x_1)^2+(y_2-y_1)^2)`

Distance between Mathtown (-2, 5) to Geometryville (3, -1)

`d_1=√((3+2)^2+(-1-5)^2)`

`=√(25+36)`

`=√(61)`

`=7.81`

Distance between Geometryville (3, -1) and Algebra Springs (-6, -5)

`d_2=√((3+6)^2+(-1+5)^2)`

`=√(81+16)`

`=√(97)`

`=9.85`

Distance between Algebra Springs (-6, -5) and Mathtown (-2, 5)

`d_3=√((6-2)^2+(5+5)^2)`

`=√(16+100)`

`=√(116)`

`=10.77`

Now total distance traveled by Kim =
`d_1+d_2+d_3`

= 7.81 + 9.85 + 10.77

= 28.43

Therefore, Option (3) will be the answer.