In an earlier unit, you worked with coordinate points in order to find distances, midpoints, and slopes using formulas. A cordinate proof was also shown. If you need to prove a figure is a particular shape, a coordinate proof can be used.
For example, if four points are given and you need to prove that the points form a rectangle, what information would you need? What are the characteristics of a rectangle? Rectangles have 2 pair of opposite sides parallel, and the pairs are not necessarily equal to each other. Rectangles also have four 90o angles, in other words the consecutive sides are perpendicular. The slope formula can determine if the slopes are equal, meaning the sides are parallel. If the slopes are opposite reciprocals, then the sides are perpendicular to each other. Using the distance formula to find the lengths of the sides can determine if the sides are equal. The following steps will be helpful when doing a coordinate proof.