Given two points A(3,1) and B(-12,-1), determine a third point P(x,y) such that the slopes of AP and BP are -2/3 and 2/3 respectively.

2 answers

slope AP = (y-1)/(x-3) = -2/3
3y-3 = -2x + 6
2x + 3y = 9

slope BP = (y+1)/(x+12) = 2/3
2x + 24 = 3y + 3
2x - 3y = -21

Solve the two equations, adding them would be the simplest way.
Thank you! Now I've got (-3,5)