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

a line segment is divided by x-axis so Y is equal to zero
let the ratio is K ratio 1
bisection formula
0=6k+ 1(-3) /k+1
0=6k-3
3=6k
3/6=k
1/2=k
therefore the ratio is 1 /2:1
now by Section formula
x=5k+2/k+1
x=5×1/2 + 2/1/2+1
x=5/2+2/3/2
x=9/2×2/3
x=3
therefore coordinates of point of intersection are (3, 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)