The slope of the line from A to A'180 is +2/5 and the slope of the line from A'90 to A'270 is -5/2. These slopes are opposite reciprocals, so these lines are perpendicular.

To get from point O to A'180, you would move DOWN 3 units and LEFT 5 units. So you do the OPPOSITE of what you did to get from point O to A. They are on the same line so they still have the same slope --> +3/+5 = -3/-5.

To get from point O to A'90, you move UP 5 units and LEFT 3 units, or +5/-3. To get from point O to A'270, you do the opposite, so move DOWN 5 units and RIGHT 3 units, or -5/+3. Both of these slopes are the opposite reciprocal of the slope of the line from point O to A.

To get to A'180, I do the opposite of what I did to get from point O to point A. So if point O to point A is UP 2 units and RIGHT 3 units, point O to A'180 is DOWN 2 units and LEFT 3 units. The slope of this line is +2/+3 or -2/-3, which reflects the movements made from point O to A and A'180.[br][br]To get to A'90 and A'270, I do the opposite reciprocal of what I did from point O to A, since these lines are perpendicular. So for A'90, from point O I would move UP 3 units and LEFT 2 units. For A'270, I do the opposite of A'90, and go DOWN 3 units and RIGHT 2 units. The slope of this line is +3/-2 or -3/+2, which reflects the movements made from point O to A'90 and A'270.