Point plotting is an elementary

mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

skill required in

analytic geometry In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineerin ...

. Invented by

René Descartes René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathem ...

and originally used to locate positions on

military A military, also known collectively as armed forces, is a heavily armed, highly organized force primarily intended for warfare. It is typically authorized and maintained by a sovereign state, with its members identifiable by their distinct ...

map A map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes. Many maps are static, fixed to paper or some other durable medium, while others are dynamic or interactive. Although ...

s, this skill is now assumed of everyone who wants to locate grid 7A on any map. Using point plotting, one associates an

ordered pair In mathematics, an ordered pair (''a'', ''b'') is a pair of objects. The order in which the objects appear in the pair is significant: the ordered pair (''a'', ''b'') is different from the ordered pair (''b'', ''a'') unless ''a'' = ''b''. (In con ...

real number In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real ...

s (''x'', ''y'') with a point in the

plane Plane(s) most often refers to: * Aero- or airplane, a powered, fixed-wing aircraft * Plane (geometry), a flat, 2-dimensional surface Plane or planes may also refer to: Biology * Plane (tree) or ''Platanus'', wetland native plant * Planes (gen ...

in a one-to-one manner. As a result, one obtains the 2-dimensional

Cartesian coordinate system A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in t ...

. To be able to plot points, one needs to first decide on a point in plane which will be called the ''origin'', and a couple of

perpendicular In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the ''perpendicular symbol'', ⟂. It can ...

lines, called the ''x'' and ''y'' axes, as well as a preferred direction on each of the lines. Usually one chooses the ''x'' axis pointing right and the ''y'' axis pointing up, and these will be named the ''positive'' directions. Also, one picks a segment in the plane which is declared to be of unit length. Using rotated versions of this segment, one can measure distances along the ''x'' and ''y'' axes. Having the origin and the axes in place, given a pair (''x'', ''y'') of real numbers, one considers the point on the ''x'' axis at distance , ''x'', from the origin and along the positive direction if ''x''≥0, and the other direction otherwise. In the same way one picks the point on the ''y'' axis corresponding to the number ''y''. The line parallel to the ''y'' axis going through the first point and the line parallel to the ''x'' axis going through the second point will intersect at precisely one point, which will be called the point with coordinates (''x'', ''y'').

See also