Find the value of k if the following equation are consistent.

$(\mathrm{k}+1)\mathrm{x}+(\mathrm{k}-1)\mathrm{y}+(\mathrm{k}-1)=0$

$(\mathrm{k}-1)\mathrm{x}+(\mathrm{k}+1)\mathrm{y}+(\mathrm{k}-1)=0$

$(\mathrm{k}-1)\mathrm{x}+(\mathrm{k}-1)\mathrm{y}+(\mathrm{k}+1) =0$

Find the value of k if the following equation are consistent.

$3\mathrm{x}+\mathrm{y}-2=0 \mathrm{kx}+2\mathrm{y}-3=0$ and $2\mathrm{x}-\mathrm{y}=3$

Find the value of $k$ if the following equation are consistent: $(k-2)x+(k-1)y=17,$$(k-1)x+(k-2)y=18$ and $x+y=5$.

Find the area of triangle whose vertices are $A(-1,2), B(2,4), C(0,0)$.

Find the area of triangle whose vertices are $P(3,6),Q(-1,3),R(2,-1)$.

Find the area of triangle whose vertices are $L(1,1),M(-2,2),N(5,4)$

Find the value of $k$, if area of triangle is $4$ sq.unit and vertices are $P(k,0), Q(4,0), R(0,2)$.

Find the value of $k$ if area of triangle is $33/2$ square unit and vertices are $L(3,-5),M(-2,k),N(1,4)$.