(Q15) In what ratio does the point (-4,6) divide the line segment joining the points A(-6,10) and B(3,-8).

Answer

Let (-4,6) divide AB internally in the ratio m1:m2 using the section formula,we get

(-4,6)= (
3m1-6m2
m1+m2
 ,
-8m1+10m2
m1+m2
)

We know that if(x,y)=(a,b) then x=a and y=b

So, -4=
3m1-6m2
m1+m2
 and 6=
-8m1+10m2
m1+m2
Now, -4=
3m1-6m2
m1+m2
 gives us

= -4m1-4m2=3m1- 6m2

i.e m1=m2

m1
m2
 =

m1:m2=:

We should verify that the ratio satisfes y-coordinate also

Now,
-8m1+10m2
m1+m2
 =
-8
m1
m2
+10
m1
m2
+1
(dividing through by m2)
=
-8
+10
+1

=
-
+10

=
-+70
 =
=

Therefore the point (-4,6) divides the line segment joining the points A(-6,10) and B(3,-8) in the ratio :