Question:
The area of the triangle formed by the line $\frac{x}{a}+\frac{y}{b}=1$ with the coordinate axes is
(a) $a b$
(b) $2 a b$
(c) $\frac{1}{2} a b$
(d) $\frac{1}{4} a b$
Solution:
Given the area of the triangle formed by the line $\frac{x}{a}+\frac{y}{b}=1$
If in the equation $\frac{x}{a}+\frac{y}{b}=1$ either $\mathrm{A}$ and $\mathrm{B}$ approaches infinity, The line become parallel to either $\mathrm{x}$ axis or $\mathrm{y}$ axis respectively,
Therefore
$x=a$
$y=b$
Area of triangle $=\frac{1}{2} \times x \times y$
$=\frac{1}{2} \times a \times b$.
Hence, the correct choice is c
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