I would appreciate some help with my geometry homework

[carojay]

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.

 

[Matterwave]

Homework questions should be posted in the homework forum. ;)

 

[carojay]

Sorry! I'm new and I looked for that but couldn't find it!

 

[Matterwave]

Here's the homework forums: https://www.physicsforums.com/forumdisplay.php?f=152

 

[thelema418]

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.

Why don't you use a combination of the things that you know. I think the point of the problem is that you know how to translate the line. Thus, you know how to move the point $(x_0, y_0)$ to $(0,0)$. Next, you say that you know how to do rotation about the origin. You can apply that concept. Finally, you just have to translate $(0,0)$ back to $(x_0, y_0)$.