Question

find the ratio in which p(4,m) divides the line segment joining the points A(2,3) and B(6,-3).Hence find m

Answer 1

Let the point P (4,m) divide the line segment joining A (2,3) and B (6,-3) in the ratio k:1.

Applying the section formula

{(mx2+nx1)/(m+n), (my2+ny1)/(m+n)},

we have (4,m) = {(6k+2)/(k+1), (-3k+3)/(k+1)}

So 4 = (6k+2)/(k+1). Solving we get k= 1.

So the ratio is 1:1. i.e., P is the mid point of AB.

Also m = (-3k+3)/(k+1) = (-3+3)/1+1 = 0. So m= 0.