Question

IN WHAT RATIO DOES THE X AXIS DIIVIDE THE LINE SEGMENT JOINING THE POINTS 2,-3 AND 5,6 ALSO FIND THE COORDINATES OF POINT OF INTERSECTION

Answer 1

Let requird ration is k:1 and point on x axis is (a, 0).
Now...using y coordinates..
0 = {k.6 + 1.(-3)}/(k+1)
or... 6k -3 = 0
or... k = 1/2
so ratio k:1= 1/2:1 = 1:2
For Point...
a = {1.5 + 2.2}/(1+2)
a= 6
so point is (a,0) = (6,0)

Answer 2

We know that

x = M1x2 +M2x1/M1+ M2

And

y = M1y2 + M2y1/M1 +M2

But we know that y=0

So

0 =6M1-3M2/M1 + M2

0 = 6M1 -3M2

-6M1 = -3M2

M1/M2 = 1/2

The ratio is 1 : 2

x = 1*5 +2*2/1+3 = 5+4 /3 =9/3 =3 The coordinate is (3,0)