A familiar example is the concept of the graph of a function. 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 x 2 + y 2 = 4.Ĭartesian 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. 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. So the point is in quadrant I.Illustration of a Cartesian coordinate plane. the ordinate is 5 and the abscissa is 3.the abscissa is -5 and the ordinate is 3.the abscissa is -5 and the ordinate is -3.the ordinate is 5 and the abscissa is -3.Without plotting the points indicate the quadrant in which they are located, if Clearly, point (3, 5) is in 1st quadrant.Clearly, point (5, 3) is in 2nd quadrant.the point (5, - 3) is in the 3rd quadrant.Clearly, point (3, 5) is in the 2nd quadrant.Read More: Section Formula in Coordinate Geometry the ordinate is 5 and the abscissa is 3 (3 Marks).the abscissa and - 5 and the ordinate is 3.the abscissa is 5 and the ordinate is - 3.the ordinate is 5 and the abscissa is - 3.Without plotting the points indicate the quadrant in which they are located, if: whose ordinate is -4 and lies on the y-axis. whose abscissa is 5 and lies on the x-axis. (abscissa of P) – (abscissa of Q) will be 1. If the coordinates of two points are P (-2, 3) and Q (-3, 5), then find (abscissa of P) – (abscissa of Q). Without plotting the points indicate the quadrant in which they will lie, if (i.) Ordinate is -3 and abscissa is -2 (ii.) Abscissa is 5 and ordinate is -6. The Abscissa is -3 and the ordinate is -4. Write abscissa and ordinate of point (-3,-4). The abscissa and ordinate of the point with coordinates (8,12) is Write the ordinate value of all points on the x-axis.