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.
$\endgroup$ 52 Answers
$\begingroup$Hint-
Step 1 - Calculate the equation of line joining $(1,3)$ and $(2,7)$.
Step 2 - Find the point of intersection of the two lines.
Step 3 - Find the ratio using the above mentioned formula and you will get the ratio.
The answer that I got is $-6:25$.
$\endgroup$ $\begingroup$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.
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