The area of the triangle formed by the line

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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