Question

Please help

The map of a biking trail is drawn on a coordinate grid.

The trail starts at P(−2, 2) and goes to Q(5, 2).
It goes from Q to R(5, −5) and then to S(8, −5).

What is the total length (in units) of the biking trail?

10
16
17
18

Answer 1

17 units

Explanation:

Distance between points
`(a,b)\,,\,(c,d)` is given by
`√((c-a)^2+(d-b)^2)`

The trail starts at P(−2, 2) and goes to Q(5, 2).

Take
`(a,b)=(-2,2)\,,\,(c,d)=(5,2)`

`PQ=√((5+2)^2+(2-2)^2)=√(7^2)=7` units

It goes from Q to R(5, −5)

Take
`(a,b)=(5,2)\,,\,(c,d)=(5,-5)`

`QR=√((5-5)^2+(-5-2)^2)=√((-7)^2)=7` units

It goes from R to S.

Take
`(a,b)=(5,-5)\,,\,(c,d)=(8,-5)`

`RS=√((8-5)^2+(-5+5)^2)=√(3^2)=3` units

`PQ+QR+RS=7+7+3=17` units