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.

Answer 1

we have

A(-3,1), B(2,3), and C(4,-1)

we know that

the distance between two points is equal to the formula

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

so

Step 1

Find the distance AB

`d=\sqrt{(3-1)^(2)+(2+3)^(2)}`

`d=\sqrt{(2)^(2)+(5)^(2)}`

`dAB=√(29)\ units`

convert units to miles

`dAB=√(29)\ miles`

Step 2

find the distance BC

`dBC=\sqrt{(-1-3)^(2)+(4-2)^(2)}`

`dBC=√(20)\\dBC=2√(5)\ units`

convert unit to miles

`dBC=2√(5)\ miles`

Step 3

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

Sum the distance AB and the half distance BC

`=√(29)\ miles+(0.5)*2√(5)\ miles\\ =5.4+2.2\\ =7.6\ miles`

therefore

the answer is

`7.6\ miles`