(Q9) Let A(4,2) , B(6,5) and C(1,4) be the vertices of △ABC.

ABCDEFP

Find the coordinates of the point P on AD such that AP:PD = 2:1.

P is a point on AD which divides AD in the ratio 2:1.

P(x,y) = (
m1x2+m2x1
m1+m2
 ,
m1y2+m2y1
m1+m2
 )
= (
2×
2
+1×
2+1
 ,
2×
2
+1×
2+1
 )
= (
7+
3
 ,
9+
3
 )
= (
3
 ,
3
 )

Mid point of the line joining the points (x1,y1) and (x2,y2).