A way to think about solving the problem

Information we have: a point P1(x1, y1) and an origin O(xo, yo). What we want to know, P2(x2,y2). Visualization that worked for me(think of singular lines): x-axis |-----------x1—----------xo—------x2—----| Formula for midpoint xo is: xo = (x2 + x1)/ 2 We have xo, so rearrange to solve for x2: New formula: x2 = 2xo - x1

Why the formula for point-reflection works: When subtracting a coordinate and changing the sign, the coordinate rotates 180 degrees. Example: given x1 = 2, assuming origin is O(0,0), the opposite of x1 would be -2, so x2 = 2(0) - 2
|--------- -2 —---------------Ox = 0 —--------------- 2 —---|

Take note of the information that you have and rearrange/find a formula to help solve the problem. Break down the diagram into something simpler.

For shapes it would be the same concept, just apply to each point.