Graph quadrilaterals

Key Notes:

Understanding Quadrilaterals

  • A quadrilateral is a four-sided polygon with four angles.
  • Common types: square, rectangle, parallelogram, rhombus, trapezoid.

Coordinate Plane Basics

  • The coordinate plane consists of an x-axis (horizontal) and a y-axis (vertical).
  • Points are plotted using ordered pairs (x, y).

Graphing a Quadrilateral

  • Identify and plot four points (vertices) on the coordinate plane.
  • Connect the points in order to form the quadrilateral.
  • Verify that the sides and angles match the given quadrilateral type.

Using Distance Formula

  • The distance between two points (x1,y1) and (x2,y2) is:

d = √(x2−x1)2+ (y2−y1)2

  • Used to check side lengths and confirm the type of quadrilateral.

Using Midpoint Formula

  • The midpoint of a line segment with endpoints (x1,y1) and (x2,y2) is:

M = ( x1 + x2 / 2 , y1 + y2 / 2 )

  • Used to find diagonals’ midpoints and check symmetry.

Using Slope Formula

  • The slope between two points (x1,y1) and (x2,y2) is:

m = y2−y1 / x2 − x1

  • Helps determine parallel and perpendicular sides.
  • Parallel lines have equal slopes, perpendicular lines have negative reciprocal slopes.

Classifying Quadrilaterals on a Graph

  • Parallelogram: Opposite sides are parallel (equal slopes) and equal in length.
  • Rectangle: Opposite sides are equal, and adjacent sides are perpendicular.
  • Rhombus: All sides are equal, and opposite sides are parallel.
  • Square: All sides are equal, adjacent sides are perpendicular.
  • Trapezoid: Only one pair of opposite sides is parallel.

Finding Area of Quadrilaterals on a Graph

  • Rectangle & Square: Use the formula A = length × width
  • Parallelogram: A = base × height
  • Trapezoid: A = 1/2 (Base1 + Base2) × Height

Transformations of Quadrilaterals

  • Translations: Shifting the quadrilateral without changing shape/size.
  • Rotations: Rotating the quadrilateral around a point.
  • Reflections: Flipping the quadrilateral across an axis.
  • Dilations: Enlarging or reducing the quadrilateral while maintaining proportion.

Learn with an example

Graph the parallelogram with vertices (8,–7), (–2,–7), (0,5) and (10,5).

Graph the point (8,–7). Start at (0, 0). Move 8 units right and 7 units down.

To draw one side of the parallelogram, graph the point (–2,–7).

To draw another side of the parallelogram, graph the point (0,5).

To complete the parallelogram, graph the point (10,5).

Graph the quadrilateral with vertices (–4,8), (–6,–3), (3,8) and (0,7).

Graph the point (4,8). Start at (0, 0). Move 4 units left and 8 units up.

To draw one side of the quadrilateral, graph the point (–6,–3).

To draw another side of the quadrilateral, graph the point (3,8).

To complete the quadrilateral, graph the point (0,7).

Let’s practice!