Constructing Rotations
A rotation is when a figure moves about a fixed point called the center point, or the center of rotation. Each vertex must move the same degree (each must have the same angle of rotation) and direction around the center point. Each vertex must be the same distance from the center. On this grid, polygon ABCDE has been rotated 180 degrees around center point (0,0) or the origin. This rotation is accurate, if you were to make the same rotation without the addition of a graph, it would look exactly the same. Without a graph you would have to first create your image, in this case I would simply draw (using a straight edge) figure ABCDE. The center of rotation is point D, so the next step is to put the point of your compass on point D and make circles that connect to each point on the pre-image. This so when you measure out 180 degrees you'll know that the prime point you're measuring will be on the circle to its corresponding point (example, point A' would be some where on the circle drawn that connects to point A). Next, connect one of the points to point D with a line segment and use the protractor to make a mark at 180 Degrees. Then draw a line from point D that meets the mark at 180 degrees, for this step use a straight edge. Make a little point wherever the line you drew intersects the circle that connects with whatever point being measured. This is the 180 degree rotation for the point that was being measured. Repeat this with all the points, connect them to get your complete image, and you are done. The rotation of 180 degrees that you get will look exactly like the image on the graph above.

Information: Rotations