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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

Sagot :

Answer:

17 units

Step-by-step explanation:

Distance between points [tex](a,b)\,,\,(c,d)[/tex] is given by [tex]\sqrt{(c-a)^2+(d-b)^2}[/tex]

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

Take [tex](a,b)=(-2,2)\,,\,(c,d)=(5,2)[/tex]

[tex]PQ=\sqrt{(5+2)^2+(2-2)^2}=\sqrt{7^2}=7[/tex] units

It goes from Q to R(5, −5)

Take [tex](a,b)=(5,2)\,,\,(c,d)=(5,-5)[/tex]

[tex]QR=\sqrt{(5-5)^2+(-5-2)^2}=\sqrt{(-7)^2}=7[/tex] units

It goes from R to S.

Take [tex](a,b)=(5,-5)\,,\,(c,d)=(8,-5)[/tex]

[tex]RS=\sqrt{(8-5)^2+(-5+5)^2}=\sqrt{3^2}=3[/tex] units

[tex]PQ+QR+RS=7+7+3=17[/tex] units

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