SOLUTION: two cities are located in the xy plane at the points A (7,5) and B (13,8). a company wishes to place a factory on a road between the cities at A and B. it is determined thatvthe co

Question 1058769: two cities are located in the xy plane at the points A (7,5) and B (13,8). a company wishes to place a factory on a road between the cities at A and B. it is determined thatvthe company can make the most money if it places the factory exactly beyween 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 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 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Line AB is equation

Distance from A to B is

You want to know the point on the line so that

and you want to substitute for y and then solve this equation for x.

square both sides.

-------not factorable so use general solution for quadratic formula.

-------Not finished. One of these will work and the other will not work. Most likely the PLUS form will be the correct choice; and then find the corresponding y value from the equation of the line AB.
Answer by MathTherapy(10552)   (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 (13,8). a company wishes to place a factory on a road between the cities at A and B. it is determined thatvthe company can make the most money if it places the factory exactly beyween 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 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.

This exact problem was submitted a while back. I gave you an answer for it then. Actually, itw's problem # 1042721.
Again, the CORRECT answer is: the coordinate point that is
I hope you know by now to IGNORE the other person's solution, if it can be called that. I hope you avoided being EXTREMELY CONFUSED with that person's so-called attempt.
If you follow that person, you're going to be so lost that not even the National Guard will be able to find you. lol
It's just a simple, simple solution that involves 2 SIMILAR TRIANGLES. That's all. Try it!! You can do it!
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
The solution by the tutor "MathTherapy" is correct.

RELATED QUESTIONS
Two cities are located in the xy-plane at the points A(8 , 9) and B(1 , 7). A company... (answered by josmiceli)
Two cities are located in the xy-plane at the points A(7, 5) and B 3(13, 8). A company... (answered by josgarithmetic,MathTherapy)
I know this question has been asked on here before, but there was no explanation on how... (answered by Alan3354)
Points A(−6,1) and B(0,4) are located in a coordinate plane. What is the... (answered by ikleyn)
Suppose that receiving stations X, Y, and Z are located on a coordinate plane at the... (answered by ikleyn)
Three friends are planning to visit each other. To optimize travel time, they want the... (answered by josmiceli)
Sam drives from City A to City B, and Richard drives from City B to City A on the same... (answered by ikleyn)
In the xy-coordinate system ,if (a,b) and (a+3,b+k) are the two points lie on the... (answered by Aldorozos,MathTherapy)