Question

question 7 of 10
a sailing course is shown on the graph below. a sailing boat starts at a, travels to b, then to c and then back to the starting point a. if the measurements on the graph are measured in kilometres, find the length of the sailing course, correct to the nearest kilometre.
a(3, 6)
b(2, 2)
c(6, 8)

Explanation:

Step1: Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ for AB

Let $(x_1,y_1)=(3,6)$ and $(x_2,y_2)=(2,2)$. Then $AB=\sqrt{(2 - 3)^2+(2 - 6)^2}=\sqrt{(-1)^2+(-4)^2}=\sqrt{1 + 16}=\sqrt{17}\approx4.123$

Step2: Use distance formula for BC

Let $(x_1,y_1)=(2,2)$ and $(x_2,y_2)=(6,8)$. Then $BC=\sqrt{(6 - 2)^2+(8 - 2)^2}=\sqrt{4^2+6^2}=\sqrt{16 + 36}=\sqrt{52}\approx7.211$

Step3: Use distance formula for CA

Let $(x_1,y_1)=(6,8)$ and $(x_2,y_2)=(3,6)$. Then $CA=\sqrt{(3 - 6)^2+(6 - 8)^2}=\sqrt{(-3)^2+(-2)^2}=\sqrt{9+4}=\sqrt{13}\approx3.606$

Step4: Calculate total length

Total length $L=AB + BC+CA\approx4.123+7.211 + 3.606=14.94\approx15$

Answer:

15