How do you perform a rotation of 180 degrees?

A rotation of 180 degrees involves flipping a point around a center point, typically the origin in a coordinate system, so that the point ends up directly opposite on the other side of that center. When you rotate a point ( (x, y) ) by 180 degrees, whether you do it clockwise or counterclockwise, the result will always be the same: the new coordinates will be ( (-x, -y) ). This means that both coordinates will change their signs.

Choosing to rotate counterclockwise aligns with the general rules of rotation in a coordinate plane, emphasizing that the transformation remains valid regardless of the direction of rotation. The result is consistent and leads to the same final coordinates as rotating clockwise.

Thus, the method of graphing the coordinate and rotating 180 degrees counterclockwise accurately captures the essence of a 180-degree rotation, leading to the proper new coordinates.