(Q25) Find the ratio in which the line segment joining the points (-3,10) and (6,-8) is divided by(-1,6).

Answer

Let the point (-1,6) divides the line segment joining the points (-3,10) and (6,-8) in a ratio m:n.

mx2+nx1
m+n
 ,
my2+ny1
m+n
 = (-1,6)

Where x1= -3, x2=6, y1=10, y2= -8

m()+n(-)
m+n
 = -1

m-n= -(m+n)= -m-n

m+m= -n+n

m=n

m
n
 =

m:n=:

The point (-1,6) divides the given line segment in a ratio of :.