Question

On a town map, each unit of the coordinate plane represents 1 mile. Three branches of a bank are located at A(−3, 1), B(2, 3), and C(4, −1). A bank employee drives from Branch A to Branch B and then drives halfway to Branch C before getting stuck in traffic. What is the minimum total distance the employee may have driven before getting stuck in traffic? Round to the nearest tenth of a mile if necessary.

The minimum total distance the employee may have driven before getting stuck in traffic is

miles.

Answer 1

7.6 miles

Explanation:

Given the coordinate points :

A(−3, 1), B(2, 3), and C(4, −1)

Distance (d) between A and B:

x1 = - 3 ; x2 = 2 ; y1 = 1 ; y2 = 3

d = √(x2 - x1)² + (y2 - y1)²

d = √(2 - (-3))² + (3 - 1)²

d = √25 + 4

d = 5.385 miles

BC :

d = √(x2 - x1)² + (y2 - y1)²

d = √(4 - 2)² + (-1 - 3)²

d = √2² + (-4²)

d = √4 + 16

d2 = 4.4721359 miles

(1/2) of d2 = 1/2 * 4.4721359 = 2.236 miles

Total distance = (5.385 + 2.236) miles

Total distance driven before getting stuck in traffic = 7.6 miles