2. A group of Japanese physicists works on a project where planar lines are in the form of solutions to equations a⋅x+b⋅y+c=0 where a , b , and c are fixed reals satisfying a2+b2≠0 . They need to know formulae for the images of the line a⋅x+b⋅y+c=0 in the following cases: 1. Under the translation by a vector B=[u,v] , 2. Under rotation about a point (x0,y0) by 180 degrees, 3. Under rotation about a point (x0,y0) by 90 degrees. Please provide those formulae and a justification for them. I know for number 1, you basically just add the vector B. for 2 and 3 I do not know whether to use point slope form and just change the slope or if I need to change the coordinates to (-y,x) for 90 degree rotation and (-x,-y) for 180 degree rotation but those are for rotation about the origin and my problem does not state that. Does the slope for a 180 degree rotation go back to the same slope? I am really confused on which direction to take.