Q. The area of the triangle bounded by the straight line $ax + by + c = 0,\ (a,\ b,\ c \neq 0)$ and the coordinate axes is
A) $\frac{1}{2}\frac{a^{2}}{|bc|}$
B) $\frac{1}{2}\frac{c^{2}}{|ab|}$
C) $\frac{1}{2}\frac{b^{2}}{|ac|}$
D) 0
Explanation
(b)
The vertices of the triangle are $A(0,\ 0),\ B\left( - \frac{c}{a},\ 0 \right)$ and $(C\left( 0,\ - \frac{c}{b} \right)$
$\therefore Area\ of\ \mathrm{\Delta}\ = \frac{1}{2}\left| \begin{matrix}
0 & 0 & 1 \\
- \frac{c}{a} & 0 & 1 \\
0 & - \frac{c}{b} & 1
\end{matrix} \right|$
$= \frac{1}{2}1\left| \left\{ \left( - \frac{c}{a} \right)\left( - \frac{c}{b} \right) - 0 \right\} \right|$
$= \frac{c^{2}}{2|ab|}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.