You can prove that the quadrilateral is a rectangle by finding out if the quadrilateral has opposite parallel sides, opposite congruent sides, and four 90 degree angles. You find out if the quadrilateral has opposite parallel sides by finding each sides slope(y2-y1)/(x2-x1). You find out if the quadrilateral has opposite congruent sides by finding each sides distance(distance formula=(y2-y1)squared+(x2-x1)squared, and that<------ is inside a radical. You find out if the quadrilateral has four 90 degree angles by seeing if each opposite sides slopes are reciprocals. Hope this helps, I'm typing this In the middle of doing A.P. history HW, so it might be kinda hard to understand.