If $O$ is the origin and $A$ and $B$ are points on the line $3 x-4 y+25=0$ such that $\mathbf{O A}=\mathbf{O B}=13$, then the area of $ riangle O A B$ (in sq units) is

Question

If $O$ is the origin and $A$ and $B$ are points on the line $3 x-4 y+25=0$ such that $\mathbf{O A}=\mathbf{O B}=13$, then the area of $	riangle O A B$ (in sq units) is

Aicharya · Accepted Answer

Required distance $O P=\left|\frac{0+0+25}{\sqrt{3^2+4^2}}\right|=\left|\frac{25}{5}\right|=5$ So, $A P=P B=12$ [By Pythagoras theorem in $\triangle A O P$ ] Area of $ \begin{aligned} \triangle O A B & =\frac{1}{2} \times 24 \times 5 \\ & =12 \times 5=60 \end{aligned} $

If $O$ is the origin and $A$ and $B$ are points on the line $3 x-4 y+25=0$ such that $\mathbf{O A}=\mathbf{O…

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