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Distance on a Coordinate Plane

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Coordinate Plane The coordinate plane or Cartesian plane is a basic concept for coordinate geometry. It describes a two-dimensional plane in terms of two perpendicular axes: x and y. The x-axis indicates the horizontal direction while the y-axis indicates the vertical direction of the plane. In the coordinate plane, points are indicated by their positions along the x and y-axes. Slopes On the coordinate plane, the slant of a line is called the slope. Slope is the ratio of the change in the y-value over the change in the x-value. You can use what you know about right triangles to find the distance between two points on a coordinate grid.
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Distance on a Coordinate Plane
Distance on a Coordinate Plane
Coordinate Plane
The coordinate plane or Cartesian plane is a basic concept for coordinate
geometry. It describes a two-dimensional plane in terms of two perpendicular
axes: x and y. The x-axis indicates the horizontal direction while the y-axis
indicates the vertical direction of the plane. In the coordinate plane, points are
indicated by their positions along the x and y-axes.
Slopes
On the coordinate plane, the slant of a line is called the slope. Slope is the ratio of
the change in the y-value over the change in the x-value.
You can use what you know about right triangles to find the distance between two
points on a coordinate grid.
Finding Distance on the Coordinate Plane
Know More About :- Raphing composite functions

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To find the distance between two points on the coordinate plane, draw the
segment that joins the points. Then make that segment the hypotenuse of a right
triangle. Use the Pythagorean Theorem to find the length of the hypotenuse,
which is the distance between the two points.
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of
numerical coordinates, which are the signed distances from the point to two fixed
perpendicular directed lines, measured in the same unit of length. Each reference
line is called a coordinate axis or just axis of the system, and the point where they
meet is its origin, usually 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,
one can specify a point in a space of any dimension n by use of n Cartesian
coordinates, the signed distances from 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.

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The invention of Cartesian coordinates in the 17th century by Rene 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 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.

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Distance on a Coordinate Plane

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