Final answer:
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.