Question

see the attached file and answer it ​

Answer 1

MATE

YOUR SOLUTION IS IN ATTACHED PICTURE ☺️

Answer 2

If the given line segment is divided by y axis than x coordinate will be 0.

So the coordinate of point of intersection Will be (0,y)

1) Ratio in which AB is divided by y axis.

Let the ratio as lamda : 1

Using internal divison formula.

0 = x2m1+ x1m2/ lamda+1

0 = 8lamda + (-4 )(1)/lamda +1

0 = 8 lamda -4

4 = 8 lamda

4/8 = lamda/1

1/2 = lamda/ 1

so ratio = 1:2

2) Co ordinate of point of intersection.

Using internal divison formula.

We have already x = 0 ( prove above)

y = y2m1 + y1m2/ m1+ m2

y = -3(1) +6(2)/1+2

y = -3+12/3

y = 3

So co ordinate are 0,3

3) Length of AB

Using distance formula.

AB = √( x2 - x1)^2 + (y2- y1)^2

AB = √(8-(-4)^2+[(-3)-6]^2

= √144+81

AB = 15 unit.