1. The problem statement, all variables and given/known data A group of American physicist works on a project where planar lines are in the form X=tP+sQ, where P and Q are two fixed different points and s, t are varying reals satisfying s+t=1. They need to know formulae 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 point C by 180 degrees 3. Under rotation about a point C by 90 degrees Please provide those formulae and a justification for them. 2. Relevant equations X=tP+sQ s+t=1 3. The attempt at a solution A translation by a vector, B will preserve length and slope, so the new formulae is X=tP+sQ+B. A rotation will preserve length, but not necessarily slope. I know that with points, a 90 degree rotation will give (x,y) -> (y,-x) and that a rotation of 180 degrees will give (x,y) -> (-x,y). I'm not sure how to use this information to get to a clear answer, with a formula and justification for it.