Point plotting
The following is archival and will be deleted once the merge is complete.
Point plotting is an elementary skill required in analytic geometry. Invented by Rene Descartes and originally used to locate positions on military maps, this skill is now assumed of everyone who wants to locate grid 7A on any map.
In mathematics, a point in the plane is designatied by a pair of real numbers, enclosed in parentheses and separated by a comma. Note that this exact same notation is used to designate an open interval of the real line, and the two uses can only be distinguished by the context.
The two numbers are called coordinates, and give the distances from a pair of (usually) perpendicular lines called coordinate axes. The vertical axis is called the y-axis and the distance from it is measured horizontally, with a positive number indicating a distance to the right, negative to the left. The horizontal axis is called the x-axis and the distance from it is measured vertically, positive above, negative below. The point where the two axes cross is called the origin. The first number used to be called the ordinate and the second number the abscissa but today they are almost always called the x and y coordinates, even if the axes themselves are labeld by a different letter. For example, the horizontal axis often indicates time, and is called the t-axis, while the time coordinate is called interchangeably the t-coordinate or the x-coordinate. The assumption is that mathematical sophistication will allow the reader to sort out the ambiguity.
The two axes usually have tick marks or hash marks to indicate the scale of measurement. The hash marks nearest the origin usually indicate one unit of measurement, but may indicate ten units, or a million units. To be useful, these marks need numbers on them, something many calculator graphs omit.
The ordered pair (3, -7), for example, indicates the point three units to the right of the y-axis and 7 units below the x-axis.
The most important skill for the beginner is to remember that the x-coordinate is the horizontal distance along the x-axis and is also the horizontal distance away from the y-axis. The y-coordinate is the vertical distance along the y-axis and is also the vertical distance away from the x-axis.
A graph is a set of plotted points, usually given by an equation. A point is on the graph if the following steps result in a correct arithmetic equality. Locate the letter to the right of the horizontal axis and replace that letter in the equation with the x-coordinate of the point. Locate the letter at the top of the vertical axis and replace that letter in the equation with the y-coordinate of the point. If the equality that results is correct, we also say that the point "satisfies" the equation. If the substitution does not result in a correct arithmetic equality, we say that the point does not satisfy the equation.
More advanced point plotting includes three dimensional analytic geometry, point plotting in higher dimensions, plotting of complex numbers in the Argand plane, and plotting using Barycentric coordinates.