Plotting Points on a Cartesian Plane

A Cartesian plane (named after French mathematician Rene Descartes, who formalized its use in mathematics) is defined by two perpendicular number lines: the Math formula-axis, which is horizontal, and the Math formula-axis, which is vertical. Using these axes, we can describe any point in the plane using an ordered pair of numbers.

The Cartesian plane extends infinitely in all directions. To show this, math textbooks usually put arrows at the ends of the axes in their drawings.

The location of a point in the plane is given by its coordinates, a pair of numbers enclosed in parentheses: Math formula. The first number Math formula gives the point's horizontal position and the second number Math formula gives its vertical position. All positions are measured relative to a "central" point called the origin, whose coordinates are Math formula. For example, the point Math formula is Math formula units to the right of the origin and Math formula units up, as shown in the figure. Negative coordinate numbers tell us to go left or down. See the other points in the figure for examples.

Math diagram

The Cartesian plane is divided into four quadrants. These are numbered from Math formula through Math formula, starting with the upper right and going around counterclockwise. (For some reason everybody uses roman numerals for this).

Math diagram

In Quadrant Math formula, both the Math formula- and Math formula-coordinates are positive; in Quadrant Math formula, the Math formula-coordinate is negative, but the Math formula-coordinate is positive; in Quadrant Math formula both are negative; and in Quadrant IV Math formula is positive but Math formula is negative.

Points which lie on an axis (i.e., which have at least one coordinate equal to Math formula) are said not to be in any quadrant. Coordinates of the form Math formula lie on the horizontal Math formula-axis, and coordinates of the form Math formula lie on the vertical Math formula-axis.

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