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
