Coordinate geometry: finding the ratio in which a line segment is divided by a line The question is:

Determine the ratio in which the line $3x + 4y - 9 = 0$  divides the line segment joining the points $A(1,3)$ and $B(2,7)$.

When I tried solving the question using section formula, which is:
 If $P$ divides the line  segment $A(x,y) B(p,q)$ in ratio $m:n$, then coordinates of $P$ are given by $$\left\lbrace \frac{mp + nx}{m+n}, \frac{mq + ny}{m+n} \right\rbrace.$$
I got the answer :
$(-6) : 25$
which I think is wrong and I'm not able to confirm it. If someone could show me their solution, I'll be really grateful.

Using your formula $x=1,y=3, p=2,q=9$ 
So, $P\left(\frac{2m+n}{m+n},\frac{9m+3n}{m+n}\right)$
Now, as the points $P,A,B$ are collinear, the are of the $\triangle PAB=0$ 
We can use this formula to calculate the area of of the triangle.  
