Step-by-step explanation:
Polygons are classified by ...
- number of sides (or vertices)
- relationship of sides to each other (parallel, perpendicular, other)
- relative angle sizes (all equal, some equal, none equal
- relative side lengths (all equal, some equal, none equal)
The number of coordinate pairs will define the number of vertices.
The differences between "adjacent" coordinate pairs can be used to find side lengths and relationships (angles, parallel, perpendicular).
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If the differences between adjacent coordinate pairs are ...
(∆x, ∆y) = (x2 -x1, y2 -y1)
then the slope of the line joining those coordinates is ∆y/∆x. (This may be "undefined" if ∆x = 0.) Two line segments with the same slope are parallel. Two line segments with slopes that have a product of -1 are perpendicular. (Two segments with slopes of 0 and "undefined" are also perpendicular.)
It can be useful on occasion to know that the angle (α) a line segment makes with the x-axis can be found from ...
α = arctan(slope)
The length of a line segment (d) can be found from the Pythagorean theorem:
d = √((∆x)² +(∆y)²)