After you guess what kind of quadrilateral is created by the four points, think about what would need to be true in order to show it.
Parallel lines (same slope)
Perpendicular lines (opposite reciprocal slopes [a/b and -b/a])
Equal lengths (use distance formula)
Slope formula: (y2-y1)/(x2-x1)
Distance: Create a right triangle, find the lengths of the legs (count the units). Once you know those two sides, you can use the pythagorean theorem to find the missing length. (a^2+b^2=c^2)