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(1, 4), and C(5, −2). 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

Answer 1

The distance between Branch A and Branch B is given by the Pythagoras theorem

AB² = (Vertical Distance)² + (Horizontal Distance)²
AB² = (4-1)² + (1 - -3)²
AB² = 3² + 4²
AB² = 9 + 16
AB² = 25
AB = 5

BC² = (Vertical distance)² + (Horizontal distance)²
BC² = (-2 - 4)² + (5-1)²
BC² = (-6)² + (4)²
BC² = 36 + 16
BC² = 52
BC = 7.21

Half way of BC = 7.21 ÷ 2 = 3.6 miles

Total distance travelled from A to B and then halfway from B to C is 3.6+5 = 8.6 miles