SOLUTION: Two cities are located in the xy-plane at the points A(7, 5) and B 3(13, 8). A company wishes to place a factory on a road between the cities at A and B. It is determined that the

Algebra ->  Human-and-algebraic-language -> SOLUTION: Two cities are located in the xy-plane at the points A(7, 5) and B 3(13, 8). A company wishes to place a factory on a road between the cities at A and B. It is determined that the       Log On


   

Question 1042721: Two cities are located in the xy-plane at the points A(7, 5) and B 3(13, 8). A company wishes to place a factory on a road between the cities at A and B. It is determined that the company can make the most money if it places the factory exactly halfway between
A and B. However, due to environmental hazards produced by the factory, it is safe for the people living in City A and City B only if the factory is located exactly one third of the distance from City A going toward City B.
Find the coordinates of the point where the factory should be placed to ensure the most ethical outcome.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
"Most ethical outcome" and "safest....one third of the dis...from A to B", means find the the point one third of the distance from A to B.

Unknown point (x,y).
sqrt%28%28x-7%29%5E2%2B%28y-5%29%5E2%29%2Fsqrt%28%2813-7%29%5E2%2B%288-5%29%5E2%29=1%2F3

3%2Asqrt%28%28x-7%29%5E2%2B%28y-5%29%5E2%29=sqrt%2825%2B9%29

sqrt%28%28x-7%29%5E2%2B%28y-5%29%5E2%29=12

Before continuing with this somewhat simplified equation, find the equation in slope-intercept form for the line containing A and B. Substitute for y in the radical equation above. Continue to solve first for x.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Two cities are located in the xy-plane at the points A(7, 5) and B 3(13, 8). A company wishes to place a factory on a road between the cities at A and B. It is determined that the company can make the most money if it places the factory exactly halfway between
A and B. However, due to environmental hazards produced by the factory, it is safe for the people living in City A and City B only if the factory is located exactly one third of the distance from City A going toward City B.
Find the coordinates of the point where the factory should be placed to ensure the most ethical outcome.
Coordinate point that's 1%2F3 from A(7, 5) to B(13, 8) or 2%2F3 from B(13, 8) to A(7, 5) is: highlight_green%28matrix%281%2C3%2C+%22%289%22%2C+%22%2C%22%2C+%226%29%22%29%29