How do you use the midpoint distance or slope formulas to help classify polygon's on the coordinate plane

The slope of two lines are equal when they are parallel to each other while if the product of two lines is -1, then, the lines are perpendicular to each other.

Let's do classification of quadrilaterals (polygon's with 4 sides):

The classification of polygon's can be done as follows:

(i) Check whether the opposite sides of polygon have equal slopes or unequal slopes. If two sides are parallel and other two are non-parallel, then it is a trapezium.

(ii) If no pair of opposite sides are parallel it is scalene quadrilateral.

(iii) If the opposite sides have equal slopes, then, opposite sides are parallel and it is a parallelogram. Also, the mid-points of diagonals will be same.