question_answer

The area of the triangle formed by the line \[\frac{x}{a}+\frac{y}{b}=1\] with the coordinate axes is

A) \[ab\]                            

B) \[2\,ab\]

C) \[\frac{1}{2}\,\,ab\]                   

D) \[\frac{1}{4}\,\,ab\]

Correct Answer: C

Solution :

    When \[y=0,\] \[\frac{x}{a}+\frac{y}{b}=1\] \[\Rightarrow \,\frac{x}{a}=1\Rightarrow x=a=OA\] When \[x=0.\] \[\frac{x}{a}+\frac{y}{b}=1\Rightarrow y=b=OB\] \[\therefore \Delta \,AOB=\frac{1}{2}\times OA\times OB\] \[=\frac{1}{2}\] ab sq. units.