Algebraically prove that a clockwise and counterclockwise rotation of 180o about the origin for triangle abc are equivalent rotations

A180 degree clockwise rotation can be mapped as two 90-degree rotations.  rotating a figure 90 degrees clockwise maps the point (x, y) to (y, -x).  doing this again maps the new point (y, -x) to (-x, -y).rotating a figure 90 degrees counterclockwise maps the point (x, y) to (-y, x).  doing this again maps the new point (-y, x) to (-x, -y).they map the points to the same location.