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

Answer: 8.6 miles

Step-by-step explanation:

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