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(2, 4), and c(4, −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. answer

Answer 1

Answer:

The minimum total distance the employee may have driven before getting stuck in traffic is 9.0 miles.

Step-by-step explanation:

Given information: a(−3, 1), b(2, 4), and c(4, −2).

On a town map, each unit of the coordinate plane represents 1 mile.

Distance formula:

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Distance between bank a and bank b is

$ab=\sqrt{(2-(-3))^2+(4-1)^2}$

$ab=\sqrt{(5))^2+(3)^2}$

$ab=\sqrt{25+9}$

$ab=\sqrt{34}$

Distance between bank b and bank c is

$bc=\sqrt{(4-2)^2+(-2-4)^2}$

$bc=\sqrt{(2)^2+(-6)^2}$

$bc=\sqrt{4+36}$

$bc=\sqrt{40}$

$bc=2\sqrt{10}$

A bank employee drives from branch a to branch b and then drives halfway to branch c before getting stuck in traffic. It means total distance employee may have driven before getting stuck in traffic is

$Distance=ab+\frac{1}{2}bc$

$Distance=\sqrt{34}+\frac{1}{2}(2\sqrt{10})$

$Distance=\sqrt{34}+\sqrt{10}$

$Distance=8.99323$

$Distance\approx 9.0$

Therefore the minimum total distance the employee may have driven before getting stuck in traffic is 9.0 miles.

Answer 2

To compute for distance from a to b:

 

Distance A = 4 miles, base of triangle formed between a and b

 

Distance B = 3 miles, height of triangle formed between a and b

 

Distance AB = (A^2 + B^2)^0.5    hypotenuse of triangle formed between a and b, or square root of (A^2 + B^2)

 

Distance AB = ((4)^2 + (3)^2)^0.5

 

Distance AB = (16 + 9)^0.5

 

Distance AB = (25)^0.5

 

Distance AB = 5 miles

 

To compute for distance from b to where bank employee got stuck

 

BC = distance from b to c

 

BC  = 4 miles

 

Total distance driven by bank employee

 

= AB + 0.5(BC)

 

= 5 + 0.5(4)

 

= 5 + 2

 

= 7 miles, total distance driven by the bank employee