The points A (7,6) and B (2,1) are 3 units and 2 units respectively from the line L and are on the opposite sides of L. Find the coordinates of the point where the interval AB crosses the line L.

Question

The points A (7,6) and B (2,1) are 3 units and 2 units respectively from the line L and are on the opposite sides of L. Find the coordinates of the point where the interval AB crosses the line L.

Answer 1

let the point be P(x,y)

then by ratios ....
(7-x)/(x-2) = 3/2
3x-6 = 14-2x
5x=20
x = 4

and

(6-y)/(y-1) = 3/2
3y-3 = 12-2y
5y = 15
y = 3

the point is (5,3)

(A nice addition to the question would be to find the equation of L )