Find the ratio in which the y-axis divides the line segment joining the points (-4, -6) and (10, 12). Also, find the coordinates of the point of division.

Using the section formula, if a point (x,y) divides the line joining the points (x1,y1) and (x2,y2) in the ratio m:n, then (x,y) = (mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)
Let y-axis divides the line joining points A(-4, -6) and B(10, 12) in ratio y:1
Then, as per section formula the coordinates of point which divides the line is (10y - 4)/(y+1), (12y - 6)/(y+1)
We know that coordinate at y-axis of point of x is zero
Then, (10y - 4)/(y+1) = 0
=> 10y - 4 = 0
=> 10y = 4
=> y = 4/10 = 5/2
Then, ratio is 2/5 : 1 => 2:5
Substitute the value of y in y-coordinates, we get (12(2/5) - 6)/(2/5 + 1) = (24 - 30)/7 = -6/7
Then, coordinates of point which divides the line joining A and B is (0, 2) and ratio 2/5.