Using the section formula, if a point (x,y) divides the line joining the points (x1,y1) and (x2,y2) in the ratio m:n, then
(x,y) = (mx2+nx1m+n,my2+ny1m+n)
Let the ratio in which the line segment joining A(-3, 10) and B(6, - 8) is divided by
P(-1, 6) be k : 1.
Then, by section formula, the coordinates of P are (6k−3k+1,−8k+10k+1)
⟹(−1,6)=(6k−3k+1,−8k+10k+1)
Therefore, −1=6k+1(−3)k+1
⇒ −k−1=6k−3
⇒ 2=7k
⇒ k=27
⇒ k:1=27:1=2:7
Therefore, the point P divides AB in the ratio 2:7.