First off, plot the vertices. When you finish, you should get the shape of a kite, to prove that it is a kite, find the slope of the line between (1,1) and (5,5), then find the slope of (6,2) and (3,6), if one of the slopes are the reciprocal and negative of the other slope, then the 2 lines are perpendicular to each other. Then, use the distant formula to find the distand between (6,2) - (5,5) and between (3,6) - (5,5). If the two lines are congruent, then you have proven that the shape is indeed a kite. Then, use the distant formula to find the necessary lines and use the kite are formula.