A point in a plane can be located by referring to its distance from two number lines which are perpendicular to each other. Such a system is called as 'Cartesian system'.
By convention, the horizontal number line is called as x - axis and is denoted by line XX'. The vertical number line is called as y - axis and is denoted by line YY'.
The point where the two lines intersect is taken to be zero on both the number lines. The intersection point is called as the origin and is denoted by 'O'.
In the image shown below, the x - axis is shown. The blue, red, green and grey lines cut the x - axis and are perpendicular to the x - axis. Which line is the YY' axis?
Answers
Answer:
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.