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(4, 3), and C(2, −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.

Answer 1

First, we determine the distance between points A and B using the formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]
d = √[(4 - -3)² + (3 - 1)²]
d = √(7² + 2²)
d = 7.28 miles

Next, the distance between B and C, using the same formula is:
d = 4.47 miles; half of which is 2.24 miles

The total minimum distance that he must drive is:
7.28 + 2.24 = 9.52 miles