Definition 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.

Click on the button "click here to start" to start the applet.

How do you use this applet?

enter the x coordinate and y coordinate and press "ENTER". To delete a point, press "DELETE POINT" and click on the point to be deleted. Repeat for every point to be deleted. To show or hide quadrant numbering, press "SHOW/HIDE QUADRANT".

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Tutorial 1:Quadrants

For each 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)

Questions 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?

Questions 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 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?