Question

Find the ratio in which origin divides PQ.Ratio being 1 : ____

Answer 1

Let us assume the origin divides PQ in the ratio m:n
Applying the section formula is,

$\frac{n\times x_1+m\times x_2}{m+n},\frac{n\times y_1+m\times y_2}{m+n})$

Where $(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of the line. Then,

$(0,0)$ = $(\frac{n\times -3+m\times 6}{m+n},\frac{n\times 2+m\times -4}{n+m})$

6m - 3n = 0
6m = 3n
m:n = 1:2
The origin divides the line PQ in the ratio 1:2.