Question

Area of $\Delta$ formed by line $3x+4y+12=0$ with co-ordinate axis is

• A. $6$
• B. $2$
• C. $1$
• D. $5$

Answer 1

The correct option is A $6$

Equation of $x-$ axis is $y=0$ ………$\left(1\right)$

Equation of $y-$ axis is $x=0$ ………$\left(2\right)$

Let given equation $3x+4y+12=0$ meets $x-$ axis at point $A$ and $y-$axis at $B$

At $A$ we have $y=0\Rightarrow 3x=-12$

$\Rightarrow x=-4$

$\therefore A$ is $(-4,0)$

$\Rightarrow OA=\sqrt{{(-4)}^2+0}=4$units

At $B$ we have $x=0\Rightarrow 4y=-12$

$\Rightarrow y=-3$

$\therefore B$ is $(0,-3)$

$\Rightarrow OB=\sqrt{0+{(-3)}^2}=3$units

Area of triangle$=\frac{1}{2}\times OA\times OB=\frac{1}{2}\times 4\times 3=6squnits$