Question

find the ratio in which the Y axis divides the line segment joining the points (5,-6) and (-1,-4). also fine these coordinate of the points of division

Answer 1

A = (5, -6)      B= (-1,  -4).

Y axis divides AB into  ratio  m : 1   let us say.  Let Y axis intersect AB at P(0, b).

So   x coordinate of P = 0 = [ 5*1 + m(-1) ] (1+m)
     =>   m = 5

Ratio =:    5  : 1

So   y coordinate of P:   y = [ -6*1 + m * (-4) ] / (1+m)
                                          = [ -6 - 20 ]/6
        = -26/6 = -13/3

Point P = (0,  -13/3)