question_answer

The Line \[\text{4x}+\text{3y}-\text{12}=0\] cuts the coordinate axes at A and B. The area of \[\Delta OAB\] is:

A) 2 sq. units

B) \[\frac{3}{2}\] sq. units

C) 6 sq. units

D) 12 sq. units

Correct Answer: C

Solution :

[c] Given line, \[4x+3y-12=0\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{x}{3}+\frac{y}{4}=1\]

The given cuts X- and V-axes at points \[(3,0)\] and \[(0,4)\] respectively.

\[\therefore \]Area of \[\Delta AOB=\frac{1}{2}\times OA\times OB\]

\[=\frac{1}{2}\times 3\times 4=6\,sq.\] units