CMAT 2021 Solved Question Paper

Given point $\left(-6,0\right)$ and $\left(-8,2\right)$
∴ Equation of line $\mathit{y}-0=\frac{2-0}{-8+6}\times \left(\mathit{x}+6\right)$
⇒ $\mathit{y}=-\left(\mathit{x}+6\right)$
⇒ $\mathit{y}+\mathit{x}=-6$ ...(i)
and equation of line passing through the points $\left(-6,0\right)$ and $\left(-8,-2\right)$ .
$\mathit{y}-0=\frac{-2-0}{-8+6}\times \left(\mathit{x}+6\right)$
⇒ $\mathit{y}=\mathit{x}+6$
⇒ $\mathit{y}-\mathit{x}=6$ ...(ii)
Similarly equation of line passing through points $\left(6,0\right)$ and $\left(8,2\right)$
$\mathit{y}-0=\frac{2-0}{8-6}\times \left(\mathit{x}-6\right)$
⇒ $\mathit{y}=\left(\mathit{x}-6\right)\Rightarrow \mathit{y}-\mathit{x}=-6...\left(\mathrm{iii}\right)$
Similarly equation of line passing through points $\left(6,0\right)$ and $\left(8,-2\right)$
$\mathit{y}=\frac{-2-0}{8-6}\times \left(\mathit{x}-6\right)\Rightarrow \mathit{y}+\mathit{x}=6$ ...(iv)
From Eqs. (i) and (iv), we get $\left|\mathit{x}+\mathit{y}\right|=6$
and from Eqs. (ii) and (iii), we get $\left|\mathit{x}-\mathit{y}\right|=6$
∴ $\left|\mathit{x}+\mathit{y}\right|-|\mathit{x}-\mathit{y}|=0$