the ratio in which y-axis divides the line joining the point P(-4,5) and Q(3,-7) is ?

Hello student,
Suppose it divides the line segment in the ratio k :1.
Then , we know that the coordinates of the point dividing the line segment joining (x₁, y₁) and (x₂, y₂) in the ratio m : n is given by
[(mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n))]
Here, (x₁, y₁) = (-4,5) and and (x₂, y₂) = (3,-7)
So, coordinates of point of intersection of PQ with y-axis (using the above formula)
=[(3k-4)/(k+1), (-7k+5)/(k+1)]
The x-coordinate of the point of the point of intersection of PQ and y-axis = 0
So, (3k-4)/(k+1) = 0
This gives k = 4/3
Hence, the required ratio is 4:3.