We have planar lines in the form of $X=tP+sQ$, where $P$ and $Q$ are two fixed different points and $s,$ $t$ are varying reals satisfying $s+t=1$. We need to find the formula for the images of the line $X=tP+sQ$ in the following three cases:
1. Under the translation by a vector B.
2. Under rotation about a pont C by 180 degrees.
3. Under rotation about a point C by 90 degrees.