ABC is dilated by a scale factor of 3 with the origin as the center of dilation to form A’B’C’. The slope of AB is -1.2. The length of AB is p units, the length of AC is q units, and the length of BC is r units. The slope of A’B’ is . The length of A’C’ is . units

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.