A quadrilateral where all interior angles are 90°, and whose location on the
coordinate plane
is determined by the
coordinates
of the four
vertices (corners).

Try this
Drag any vertex of the rectangle below. It will remain a rectangle and its dimensions calculated from its coordinates.
You can also drag the origin point at (0,0).

A rectangle is similar to an ordinary rectangle
(See Rectangle 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 width, height etc can be found.

It has all the same properties as a familiar rectangle:

- Opposite sides are parallel and congruent
- The diagonals bisect each other
- The diagonals are congruent

The dimensions of the rectangle 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 rectangle 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 rectangle is rotated on the plane, as in the figure above. But
if the sides of the rectangle 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

**The height**of the rectangle 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

- In the figure at the top of the page, click on "hide details" .
- Then drag the corners to create an arbitrary rectangle.
- Calculate the width, height and the length of the diagonals.
- Click 'show details' and "show diagonals" to verify your answer.

In the interest of clarity in the applet above, the coordinates are rounded off to integers and the lengths rounded to one decimal place. This can cause calculatioons to be slightly off.

For more see Teaching Notes

- 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 - Line (Coordinate Geometry)
- Ray (Coordinate Geometry)
- Segment (Coordinate Geometry)
- Midpoint Theorem

- Cirumscribed rectangle (bounding box)
- Area of a triangle (formula method)
- Area of a triangle (box method)
- Centroid of a triangle
- Incenter of a triangle
- Area of a polygon
- Algorithm to find the area of a polygon
- Area of a polygon (calculator)
- Rectangle
- Square
- Trapezoid
- Parallelogram

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