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. 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. The equation of a circle is ( x − a) 2 + ( y − b) 2 = r 2 where a and b are the coordinates of the center ( a, b) and r is the radius. These coordinates are equal, up to sign, to distances from the point to n mutually perpendicular hyperplanes.Ĭartesian coordinate system with a circle of radius 2 centered at the origin marked in red. In general, n Cartesian coordinates (an element of real n-space) specify the point in an n-dimensional Euclidean space for any dimension n. 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). 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. Each reference coordinate 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). 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.Ī Cartesian coordinate system ( UK: / k ɑː ˈ t iː zj ə n/, US: / k ɑːr ˈ t i ʒ ə n/) 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. A coordinate pair of (-3, -3) will be in Quadrant III because both the x-value and the y-value are positive.Illustration of a Cartesian coordinate plane. Knowing the characteristics for each of the quadrants means you can place a list of plot points simply by looking at the x values and y values and seeing whether they are positive numbers or negative numbers.įor example, a coordinate pair of (1, 4) will be in Quadrant I because both the x-value and y-value are positive. Understanding the Four Coordinate Plane Quadrants Here are the characteristics for each of the four coordinate plane quadrants: For the y-axis, a positive y-coordinate will be on the top half and a negative y-coordinate will be on the bottom half. On the x-axis, a positive x coordinate will be in the right quadrants and a negative x coordinate will be in the left quadrants. Each axis is a number line (horizontal number line for the x-axis, and vertical number line for the y-axis) that goes on forever in the negative direction (negative infinity) and positive direction (positive infinity). In each pair of numbers, the first number represents the x-coordinate, and the second number represents the y-number. Characteristics of Each of the Coordinate Plane QuadrantsĪs we know, each ordered pair of a point on the graph has an x-coordinate and a y-coordinate. The four coordinate plane quadrants don't have names but are simply known as the first quadrant, second quadrant, third quadrant, and fourth quadrant. The coordinate plane, also known as the coordinate grid, cartesian coordinate system, or Cartesian plane, is constructed by taking a vertical axis, or the y-axis and setting it against a horizontal axis, or the x-axis. There are four coordinate plane quadrants you’ll need to know when plotting points or graphing lines on the coordinate plane.
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