(Q10) Let A(4,2) , B(6,5) and C(1,4) be the vertices of △ABC.

ABCDEFP

Find the points which divide the line segment BE in the ratio 2:1 and also that divide the line segment CF in the ratio 2:1.

Given B (6 , 5) , E(
5
2
 ,3)
P(x,y) = (
m1x2+m2x1
m1+m2
 ,
m1y2+m2y1
m1+m2
 )
= (
2×
2
+1×
2+1
 ,
2×+1×
2+1
 )
= (
+6
3
 ,
+5
3
 )
= (
3
 ,
3
 )
Similarly, let P divide C(1,4) and F (5,
7
2
 ) in the ratio 2:1.
Then P = (
2 x 5 + 1 x 1
2 + 1
 ,
2 x (
7
2
 ) + 1 x 4
2 + 1
 )
= (
10 + 1
3
 ,
7 + 4
3
 ) = (
11
3
 ,
11
3
 )