Distance Traveled. A grand tour of four cities begins at city A and makes successive stops at cities B, C, and D before returning to city A. If the cities are located as shown in the figure, find the total distance covered on the tour.

Question

Quizplus · Accepted Answer

We can use the distance formula to find the distance between each pair of cities:

AB = $\sqrt{(3-1)^2 + (5-0)^2}$ = $\sqrt{14}$
BC = $\sqrt{(6-3)^2 + (4-5)^2}$ = $\sqrt{10}$
CD = $\sqrt{(4-6)^2 + (1-4)^2}$ = $\sqrt{10}$
DA = $\sqrt{(1-4)^2 + (0-1)^2}$ = $\sqrt{10}$

So the total distance is:

AB + BC + CD + DA = $\sqrt{14} + \sqrt{10} + \sqrt{10} + \sqrt{10}$
= 6$\sqrt{10}$
= about 6,000 miles (rounded to the nearest thousand)