Question

In what ratio is the line joining (2, -4) and
,
-3, 6) divided by the y-axis ?
​

Answer 1

I think formula is a common way, but I will use geometry here.

If we plot two points and the y-axis we will have three points.

(2,-4)

(0,y) [y-axis]

(-3,6)

Now, the abscissa of the three points is 2, 0, and -3. The y-axis is going to divide two lines in the ratio of 2:3.

More information:

The approach of my answer is based on triangles. If you don't understand, see the attachment.

→ Alternative Approach

The line passing through (2,-4) and (-3,6) is y=2x.

So the point on the y-axis, (0,0), divides the line into two.

The ratio of the line is 2:3.