An online graphing calculator to graph points in rectangular coordinate system. Through these tutorials, you will be able to explore the properties of points and quadrants in rectangular coordinate systems. If needed, Free graph paper is available.

Definition of Rectangular Coordinate System

A rectanguler coordinate system, or Cartesian plane, is a set of two intersecting and perpendicular axes forming an xy plane. The horizontal axes is usually labeled the x axis and the vertical axes is usually labeled the y axis. The two axes divide the plane into four parts called quadrants. Any point on the plane corresponds to an ordered pair (x,y) of real numbers x and y. x is called the x coordinate and y is called the y coordinate. Below is an applet that you may use to interactively explore points in a rectangular coordinate system.

Plot Points in Rectangular Coordinate System

enter the x coordinate and y coordinate and press "Plot Point".

Tutorial 1 - Quadrants in Rectangular Coordinate System

For each point or ordered pair, enter x and y and plot the cooresponding point.Determine the quadrant or axis where each point is located.
(2 , 3) , (-2 , -1) , (0 , -2) , (2 , -1) , (0 , 0) , (-2 , 3) , (2 , 0)
(-2 , 2) , (0 , 3) , (1 , -2) , (2 , 1) , (-3 , 0) , (-2 , -3) , (2 , -2)

Question Part 1 - (see answers below)

Use the results in the above tutorial, and perhaps some other points, to answer the follwoing questions.
1 - For what values of x and y is the point (x,y) situated in quadrant I?
2 - For what values of x and y is the point (x,y) situated in quadrant II?
3 - For what values of x and y is the point (x,y) situated in quadrant III?
4 - For what values of x and y is the point (x,y) situated in quadrant IV?
5 - For what values of x and y is the point (x,y) on the x axis?
6 - For what values of x and y is the point (x,y) on the y axis?

Question Part 2

For each situation give the coordinates of the point and use the applet to check your answer.(Note: These questions have an infinite number of possible answers).
1 - point (x,y) is situated in quadrant II.
2 - point (x,y) is situated in quadrant IV.
3 - point (x,y) is on the x axis.
4 - point (x,y) is situated in quadrant III.
5 - point (x,y) is situated in quadrant I.
6 - point (x,y) is on the y axis.

Answers to Above Questions in Part 1

1 - A point (x,y) such that x > 0 and y > 0 is situated in quadrant I.
2 - A point (x,y) such that x < 0 and y > 0 is situated in quadrant II.
3 - A point (x,y) such that x < 0 and y < 0 is situated in quadrant III.
4 - A point (x,y) such that x > 0 and y < 0 is situated in quadrant IV.
5 - A point (x,y) such that y = 0 is situated the x axis?
6 - A point (x,y) such that x = 0 is situated the y axis?