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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.

1 Answer

2 votes

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

User Zack Lee
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