Final answer:
To find the minimum total distance the bank employee may have driven, we calculated the distances AB (approximately 5.4 miles) and BC (approximately 4.5 miles), then computed half of BC since the employee only traveled halfway to C. Summing AB and half of BC gives a total of 7.65 miles, which rounds to 7.7 miles.
Step-by-step explanation:
The question involves finding the minimum total distance that a bank employee may have driven based on provided coordinates on a map, where each unit represents 1 mile. To calculate the distance between two points (A and B), we use the distance formula: √((x2-x1)² + (y2-y1)²). The employee drives from A(-3,1) to B(2,3), and then halfway to C(4,-1) from B.
First, we calculate the distance AB using the distance formula:
- AB = √((2 - (-3))² + (3 - 1)²)
- AB = √((5)² + (2)²)
- AB = √(25 + 4)
- AB = √29 ≈ 5.4 miles
Next, we calculate the distance BC:
- BC = √((4 - 2)² + ((-1) - 3)²)
- BC = √((2)² + (-4)²)
- BC = √(4 + 16)
- BC = √20 ≈ 4.5 miles
Since the employee drives only halfway to C, we take half of BC as the second leg of the journey:
Halfway to C = BC / 2 ≈ 4.5 miles / 2 = 2.25 miles
Adding both legs of the journey gives the minimum total distance the employee has driven:
Total distance = AB + Halfway to C ≈ 5.4 miles + 2.25 miles = 7.65 miles
Rounded to the nearest tenth, the employee may have driven 7.7 miles before getting stuck in traffic.