Find the area of the triangle formed by the lines `y-x=0,x+y=0`and `x-k=0`.

Explanation

Given line,
`y-x=0`…`(1)`
`x+y=0`….`(2)`
`x-k=0`…..`(3)`
Solving two-two equations, points of intersection `A=(0,0)`, `B(k,k)` and `C=(k,-k)`
Now, area of `DeltaABC`,
`=(1)/(2)|[x_(1)(y_(2)-y_(3))+x_(2)(y_(3)-y_(1))+x_(3)(y_(1)-y_(2))]|`
`=(1)/(2)|[0(k+k)+k(-k-0)+k(0-k)|`
`=|(1)/(2)(o-k^(2)-k^(2))|=|-k^(2)|`
`=k^(2)` square unit