Question

in what ratio is the line segment joining A(-2,-3)&B(5,6) dividedy-axis also find the coordinate of the point of division.

Answer 1

The equation of the line is y= 9/7 x-3/7 cutting the y axis at C(0,-3/7). length of AB is sart(130)=11.4 and of AC=3.26. Ratio AC:AB is 3.26:11.4

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)