Find the co-ordinates of a point which divides the line segment joining the points (5, 1) and (-10, 11) in the ratio 2 : 3 internally.

Explanation

Let the co-ordinates of required point be (x, y).
Here, ` " "(x_(1),y_(1))=(5, 1) and (x_(2), y_(2))=(-10, 11)`
and `" "m:n=2:3`
`" "x=(mx_(2)+nx_(1))/(m+n)=(2(-10)+3(5))/(2+3)=(-20+15)/(5)=(-5)/(5)=-1`
and `" "y=(my_(2) +ny_(1))/(m+n)=(2(11)+3(1))/(2+3)=(22+3)/(5)=(25)/(5)=5`
` therefore` Co-ordinates of required point =(-1, 5)