Question

The sides of a triangle are given by the equation $y-2=0,y+1=3(x-2)$ & $x+2y=0$. Find graphically the area of triangle.

Answer 1

$x+2y=0⟶\left(i\right)$

$y-2=0⟶\left(ii\right)$

$y+1=3(x-2)\left(iii\right)$

solving $\left(i\right)\&\left(ii\right)$

$y=2$

$x=-4$

$\therefore A=(-4,2)$

solving $\left(ii\right)\&\left(iii\right)$

$y=2$ $\Rightarrow B=(3,2)$

$x=3$

solving $\left(i\right)\&\left(iii\right)$

$\Rightarrow y+1=3(-2y-2)$

$\Rightarrow y+1=-6$

$\Rightarrow 7y=-7$

$\Rightarrow y=-1$

$\Rightarrow x=2$

$\therefore c=(2,-1)$

$\Rightarrow AB=\sqrt{49+0}=7$

Distance of c from $AB=h$

$=3units$

$\therefore$ Area $=\frac{1}{2}\times 7\times 3=\frac{21}{2}=10.5squnits$

Hence, the answer is $10.5squnit.$