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(4, 3), and c(2, −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 if necessary.

Distance formula : sqrt ((x2 - x1)^2 + (y2 - y1)^2)
(-3,1)...x1 = -3 and y1 = 1
(4,3)...x2 = 4 and y2 = 3
now we sub
d = sqrt ((4 - (-3)^2 + (3 - 1)^2)
d = sqrt ((4 + 3)^2 + (2^2))
d = sqrt (7^2 + 2^2)
d = sqrt (49 + 4)
d = sqrt 53
d = 7.28 ...so its 7.28 miles from A to B

d = sqrt ((x2 - x1)^2 + (y2 - y1)^2)
(4,3)...x1 = 4 and y1 = 3
(2,-1)...x2 = 2 and y2 = -1
now we sub
d = sqrt ((2 - 4)^2 + (-1 - 3)^2)
d = sqrt (-2^2) + (-4^2)
d = sqrt (4 + 16)
d = sqrt 20
d = 4.47but the employee only drives halfwayso this trip was 4.47/2 = 2.235

so the minimum total distance is : 7.28 + 2.235 = 9.515  rounds to 9.5 miles

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