In coordinate geometry, a parallelogram is similar to an ordinary parallelogram (See parallelogram definition ) with the addition that its position on the coordinate plane is known. Each of the four vertices (corners) have known coordinates. From these coordinates, various properties such as its altitude can be found.

It has all the same properties as a familiar parallelogram:

• Opposite sides are parallel and congruent
• The diagonals bisect each other
• Opposite angles are congruent

Dimensions of a parallelogram

The dimensions of the parallelogram are found by calculating the distance between various corner points. Recall that we can find the distance between any two points if we know their coordinates. (See Distance between Two Points ) So in the figure above:

• The height of the parallelogram is the distance between A and B (or C,D).
• The width is the distance between B and C (or A,D).
• The length of a diagonals is the distance between opposite corners, say B and D (or A,C since the diagonals are congruent).

This method will work even if the parallelogram is rotated on the plane, as in the figure above. But if the sides of the parallelogram are parallel to the x and y axes, then the calculations can be a little easier.
In the above figure uncheck the "rotated" box to create this condition and note that:

• The height is the difference in y-coordinates of any top and bottom point - for example A and B.
• The width is the difference in x-coordinates of any left and right point - for example B and D

Example

• The height of the parallelogram is the distance between the points A and B. (Using C,D will produce the same result). Using the formula for the distance between two points, this is
• The width is the distance between the points B and C. (Using A,D will produce the same result). Using the formula for the distance between two points, this is
• The length of a diagonals is the distance between B and D. (Using A,C will produce the same result). Using the formula for the distance between two points, this is

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Things to try

Other Coordinate Geometry entries

• Introduction to coordinate geometry
• The coordinate plane
• The origin of the plane
• Axis definition
• Coordinates of a point
• Distance between two points

• Introduction to Lines in Coordinate Geometry
• Lines (in Coordinate Geometry)
• Rays (in Coordinate Geometry)
• Line Segments (in Coordinate Geometry)
• Midpoint of a line segment (Midpoint Theorem)

• Distance from a point to a line - introduction
• - When line is horizontal or vertical
• - Using two line equations
• - Using trigonometry
• - Using a formula

• Slope (m) of a line
• Intercept (b) of a line
• Equation of a line in slope-intercept form y=mx+b
• Equation of a line in point-slope form y=m(x-Px)+Py

• Vertical lines
• Horizontal lines
• Parallel lines
• Perpendicular lines
• Intersecting lines

• Cirumscribed rectangle (bounding box)
• Area of a triangle (formula method)
• Area of a triangle (box method)
• Area of a polygon
• Algorithm to find the area of a polygon
• Area of a polygon (calculator)
• Rectangle
• Definition and properties, diagonals
• Area and perimeter
• Square
• Definition and properties, diagonals
• Area and perimeter
• Trapezoid
• Definition and properties, altitude, median
• Area and perimeter
• Parallelogram
• Definition and properties, altitude, diagonals

• Print blank graph paper