To begin introducing the mathematical framework for motion control, we first recall the basics of planar plots.

A point on a planar plot is denoted by a pair of numbers called coordinates or a coordinate pair. The first number expresses how far the point is in the x-direction from the y-axis and the second number expresses how far the point is in the y-direction from the x-axis. It is convenient to write the pair of numbers in a column or a row. For example, points A, B, C, and D on the figure are given by

or alternatively A = (-2,-2), B = (1,1), etc.

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The following is an interactive window that allows you to enter the coordinates of a point and see where the point lies in the x-y plane. You can also place points on the coordinate plane by clicking on the plane. The x and y coordinates of the point at which you clicked is shown also.

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Enter a value for the x coodinate and y coordinate in the appropriate text box and press "Submit" to see the point in the x-y plane. The coordinates of a point on the graph can be obtained by clicking anywhere on the graph. The applet returns the x and y coordinates of the point that you clicked. To clear entries press "Clear". To zoom in or zoom out, click the appropriate button.