I tried solving the following question, could you have a look at my answer and tell me whether it's right or wrong? All input is appreciated.
Question: Let $ABCD$ be the vertexs of a parallelogram in the affine plane immersed in its projective closure. Find the equation of the line at infinity in the projective reference ${A,B,C;D}$.
My answer: In the affine plane, $A=(0,0), B=(1,0), C=(0,1), D=(1,1)$ since $ABCD$ is a parallelogram, and their projective coordinates are $A=(1,0,0)$, $B=(1,1,0)$, $C=(1,0,1)$, $D=(1,1,1)$. Therefore the line at infinity in this reference is $2x_0+x_1+x_2=0$
