Rectangular Coordinates

Maps can be drawn using Cartesian coordinates (also known as rectangular coordinates), which are used to represent points on a two-dimensional (2D) surface as well as positions on a three-dimensional (3D) space using points on a two-dimensional (2D) surface. René Descartes, a French mathematician and philosopher, is credited with inventing the method, and his name is given to it in honour of one of the first people known to have utilised it (1596-1650). Computer displays, 3D models, and virtual reality (VR) representations all require Cartesian coordinates to define the positions of objects on screen. In addition to mathematics, physics, engineering, navigation, robotics, economics, and other sciences, the coordinate system is used in many other fields.

The Cartesian plane consists of two perpendicular axes that cross at a central point known as the origin, creating a triangle. East/west and north/south displacements from the origin are used to obtain the positions or coordinates of points on the earth.

What Are the Formulas to Convert Polar Coordinates to Rectangular Coordinates?

Consider the following for a two-dimensional system:

• There is a point A with the coordinates (x, y) in the plane

• The distance between the origin (0,0) and the point A is denoted by the letter r

• The line connecting the origin and the point A forms an angle with the positive x-axis of the coordinate system

The polar coordinates are denoted by the letters (r, θ ) while the rectangular coordinates are denoted by the letters (x, y) while the rectangular coordinates are denoted by the letters (x, y).

The conversion formulas for polar to rectangular coordinates are given as:

            X = r cosθ

            Y = r sinθ

Coordinate system

One dimension

In order to choose a Cartesian coordinate system for a one-dimensional space — that is, for a straight line — one must first choose a point O on the line (the origin), then a unit of length, and finally an orientation for the line. It is determined by an orientation which of the two half-lines indicated by O will be the positive half, and which will be the negative half; it is then said that the line “is oriented” (or “points”) from the negative half to the positive half. Then, for each point P on the line, the distance between it and the origin O can be stated by a + or a minus sign, depending on which half-line contains P.

A number line is a line that has been drawn using a certain Cartesian system.

Two dimension

Two-dimensional Cartesian coordinate systems (also known as rectangular coordinate systems or orthogonal coordinate systems) are defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. Cartesian coordinate systems in three dimensions are defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. The point at which the axes come together is chosen as the origin for both, resulting in each axis being transformed into a number line. Any point P is represented by a line through it that is perpendicular to each axis, and the point at which the line meets the axis is interpreted as a number. The Cartesian coordinates of P are represented by the two numbers in that particular order. The reverse construction allows one to find the point P given its coordinates by using the opposite method.

Three dimension

Three-dimensional Cartesian coordinate systems consist of an ordered triplet of lines (the axes) that all pass through the same point (the origin) and are pairwise perpendicular to one another; an orientation for each axis; and the same unit of length for all three axes. Cartesian coordinate systems are used to represent three-dimensional space. A number line is created for each axis, just as it is in the two-dimensional case. For any point P in space, one considers a hyperplane through P that is perpendicular to each of the coordinate axes, and the point where the hyperplane cuts the axis is represented numerically as a point on the hyperplane. P’s Cartesian coordinates are represented by those three numbers, in the sequence in which they were picked. The point P is determined by using the reverse construction, which takes its three coordinates as input.

Conclusion

In the rectangular coordinate system, two real number lines connect at a right angle to form a rectangle coordinate system. Maps can be drawn using Cartesian coordinates (also known as rectangular coordinates), which are used to represent points on a two-dimensional (2D) surface as well as positions on a three-dimensional (3D) space using points on a two-dimensional (2D) surface. The Cartesian plane consists of two perpendicular axes that cross at a central point known as the origin, creating a triangle.

In order to choose a Cartesian coordinate system for a one-dimensional space — that is, for a straight line — one must first choose a point O on the line (the origin), then a unit of length, and finally an orientation for the line.

Two-dimensional Cartesian coordinate systems (also known as rectangular coordinate systems or orthogonal coordinate systems) are defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis.

Three-dimensional Cartesian coordinate systems consist of an ordered triplet of lines (the axes) that all pass through the same point (the origin) and are pairwise perpendicular to one another; an orientation for each axis; and the same unit of length for all three axes.