The plane is also known as
a)coordinate plane
b)xy-plane
c)cartesian plane
d)all of the above
Answers
Answer:this is very long answer lol
Step-by-step explanation:
Cartesian coordinate system
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Illustration of a Cartesian coordinate plane. Four points are marked and labeled with their coordinates: (2, 3) in green, (−3, 1) in red, (−1.5, −2.5) in blue, and the origin (0, 0) in purple.
A Cartesian coordinate system (UK: /kɑːˈtiːzjən/, US: /kɑːrˈtiʒən/) 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 the same unit of length. Each reference line is called a coordinate axis or just axis (plural axes) of the system, and the point where they meet is its origin, at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.
One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, n Cartesian coordinates (an element of real n-space) specify the point in an n-dimensional Euclidean space for any dimension n. These coordinates are equal, up to sign, to distances from the point to n mutually perpendicular hyperplanes.
Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is (x − a)2 + (y − b)2 = r2 where a and b are the coordinates of the center (a, b) and r is the radius.
The invention of Cartesian coordinates in the 17th century by René Descartes (Latinized name: Cartesius) revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. Using the Cartesian coordinate system, geometric shapes (such as curves) can be described by Cartesian equations: algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2, centered at the origin of the plane, may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4.
Cartesian coordinates are the foundation of analytic geometry, and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra, complex analysis, differential geometry, multivariate calculus, group theory and more. A familiar example is the concept of the graph of a function. Cartesian coordinates are also essential tools for most applied disciplines that deal with geometry, including astronomy, physics, engineering and many more. They are the most common coordinate system used in computer graphics, computer-aided geometric design and other geometry-related data processing.
Contents
1 History
2 Description
2.1 One dimension
2.2 Two dimensions
2.3 Three dimensions
2.4 Higher dimensions
2.5 Generalizations
3 Notations and conventions
3.1 Quadrants and octants
4 Cartesian formulae for the plane
4.1 Distance between two points
4.2 Euclidean transformations
4.2.1 Translation
4.2.2 Rotation
4.2.3 Reflection
4.2.4 Glide reflection
4.2.5 General matrix form of the transformations
4.3 Affine transformation
4.3.1 Scaling
4.3.2 Shearing
5 Orientation and handedness
5.1 In two dimensions
5.2 In three dimensions
6 Representing a vector in the standard basis
7 Applications
8 See also
9 References
10 Sources
11 Further reading
12 External links
Representing a vector in the standard basis
A point in space in a Cartesian coordinate system may also be represented by a position vector, which can be thought of as an arrow pointing from the origin of the coordinate system to the point.[11] If the coordinates represent spatial positions (displacements), it is common to represent the vector from the origin to the point of interest as {\displaystyle \mathbf {r} }\mathbf {r} . In two dimensions, the vector from the origin to the point with Cartesian coordinates (x, y) can be written as: