What is the most well-known coordinate system?
T
he most well-known coordinate system is the Cartesian coordinatesystem.
Cartesian coordinates (as part of Cartesian geometry) are determined by
locating a point using the distances (measured in various units) from perpendic-
ular axes. This system uniquely marks the position of a point on a plane by using
two numbers (Cartesian coordinates), or in three-dimensional space by using
three numbers—thus giving their distances from two or three mutually perpen-
dicular lines (Cartesian axes).How are three-dimensional Cartesian coordinatesdetermined?
The three-dimensional coordinates are those that describe a solid or three-dimension-
al object with three axes (or three planes): the usual two axes (as in the two-dimen-
sional system), and an additional line. The coordinates are usually written in terms of
x, y,and z,and are often called ordered triplesor just triples.
What are some termsused in the Cartesian coordinate systemand graphs?
There are numerous terms used in the Cartesian coordinate system. Besides the ones
already mentioned, the following are some of the most common.
An interceptis a point’s distance on a coordinate system axis from the origin to
where a curve or surface intersects the axis. On a graph, the x-intercept and y-inter-
cept are two important features that show where a line cuts through the xand yaxes,
respectively. The originis the fixed point from which measurements are taken. In
most cases—especially in a standard, simple two-dimensional Cartesian coordinate
system—this means the point that represents zero. This is often seen as (0, 0), or the
point in which the xand yaxes intersect on a graph. In a three-dimensional system,
the coordinates are often seen as (0, 0, 0).
A Cartesian plane(or coordinate plane) is described as a two-dimensional space
made up of points that are identified by their relation to the origin (zero), and the x
and yaxes. An axis(the plural is axes) is a reference line used in a graph or a coordi-
nate system, such as the Cartesian system. For example, the x-axis and y-axis are per-
pendicular lines on a graph in a two-dimensional system; in a three-dimensional sys-
tem, they are the x-axis, y-axis, and z-axis.
Collinear pointsare those that lie on a straight line. Any two points are consid-
ered collinear because a straight line passes through both. Many procedures in analyt-
ic geometry involve determining the collinear points that represent coordinates that
solve an equation. Logically, those points that do not lie on the same line—or, in other
words, that do not solve the equation—are called non-collinear points. 195