Question

On a town map, each unit of the coordinate plane represents 1 mile. Three beaches of a bank are located at A(-3,1), B(4,4), and C(2,-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.

a) 9.5 miles
b) 9.9 miles
c) 10.2 miles
d) 10.6 miles

Answer 1

The employee may have driven a total of 10.8 miles before getting stuck in traffic, which rounds to 10.8 miles to the nearest tenth. This is the sum of the distance from Branch A to B and then half the distance to Branch C.

Step-by-step explanation:

The question involves finding the minimum total distance driven by a bank employee who first travels from Branch A to Branch B and then halfway to Branch C on a coordinate plane where each unit represents 1 mile.

First, we find the distance between A(-3,1) and B(4,4) using the distance formula:

dAB = √[(4 - (-3))^2 + (4 - 1)^2] = √[49 + 9] = √[58] ≈ 7.6 miles

Then, we determine the coordinates for the midpoint between B and C:

Midpoint M = ((4+2)/2, (4+(-2))/2) = (3,1)

Next, we find the distance between B and M:

dBM = √[(3 - 4)^2 + (1 - 4)^2] = √[1 + 9] = √[10] ≈ 3.2 miles

Finally, we add the distances for AB and BM:

Total distance = 7.6 miles + 3.2 miles = 10.8 miles

However, it seems there is a discrepancy as the answer does not match the provided options. Therefore, we should double-check the calculations to ensure accuracy. After reevaluation, we find that the correct answer is:

Distance AB ≈ 7.6 miles (unchanged)

Distance BM is now √[(3 - 4)^2 + (1 - 4)^2] = √[1 + 9] = √[10] ≈ 3.2 miles (unchanged)

The new total distance is 7.6 miles + 3.2 miles = 10.8 miles, which needs to be rounded to the nearest tenth resulting in 10.8 miles as the final answer.