Question

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(1, 3), and C(5, −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.

Answer 1

From A to B...
distance formula : sqrt ((x2 - x1)^2 + (y2 - y1)^2
(-3,1)....x1 = -3 and y1 = 1
(1,3)....x2 = 1 and y2 = 3
sub
d = sqrt ((1 - (-3)^2 + (3 - 1)^2
d = sqrt ((1 + 3)^2 + 2^2
d = sqrt (4^2 + 2^2)
d = sqrt (16 + 4)
d = sqrt 20
d = 4.47 miles...so from A to B, it was 4.47 miles

from B to C
d = sqrt ((x2 - x1)^2 + (y2 - y1)^2
(1,3)....x1 = 1 and y1 = 3
(5,-1)...x2 = 5 and y2 = 1
sub
d = sqrt ((5 - 1)^2 + (-1 - 3)^2
d = sqrt ((4^2 + (-4^2)
d = sqrt (16 + 16)
d = sqrt 32
d = 5.66......but keep in mind, he only drove half-way...so 5.66/2 = 2.83 miles

for a total of : 4.47 + 2.83 = 7.3 miles <===