Rotation about a point
This transformation is a rotation around point J. The rotation is performed on shape ABCDEFGHI to create shape A'B'C'D'E'F'G'H'I'. It is 182 degrees counterclockwise. The properties needed for this transformation to be a rotation are...the pre-image and the image have sides of the same length and angles of the same measure...the angle created between each set of corresponding points and the center of rotation is the same for each set of corresponding points. With a coordinate grid, to prove this is a rotation, the first thing that needs to be done is to find the center of rotation. To do this, connect a set of corresponding points and find the perpendicular bisector of that line, do this to another set. The point at which the two bisectors intersect is the center of rotation. Now, connect a point to that center and its corresponding point to that center and measure the angle created, do this to all sets of points. If each angle is the same then the transformation is a rotation.