Classify a Quadrilateral From Coordinates

How to classify a quadrilateral from coordinates

1. Plot or read the four points carefully. Label them in order around the shape so the sides do not cross. A correct order matters for deciding the type of quadrilateral.

2. Find the slopes of the sides. Use the slope formula between consecutive vertices. Compare opposite sides and adjacent sides:

   • Equal slopes mean sides are parallel.
   • Negative reciprocal slopes mean sides are perpendicular.

3. Find side lengths if needed. Use the distance formula between consecutive points. This helps you tell whether the figure has:

   • all four sides equal,
   • only opposite sides equal,
   • two pairs of equal adjacent sides, or
   • no equal sides.

4. Match the properties to the name. Common outcomes include:

   • Parallelogram: both pairs of opposite sides are parallel.
   • Rectangle: opposite sides are parallel and one angle is right.
   • Rhombus: all sides are equal and opposite sides are parallel.
   • Square: all sides equal and one right angle.
   • Trapezoid: at least one pair of opposite sides is parallel.
   • Kite: two pairs of adjacent equal sides.

Check your answer

Recheck the slopes and distances in a consistent order. If the answer can be named more than one way, choose the most specific classification supported by the coordinates.