What is Coordinate Geometry ?

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates. The coordinates’ order is important, and often they are recognised by their place in an ordered tuple or by a letter, as in “the x-coordinate.” In elementary mathematics, the coordinates are assumed to be real numbers, although they could instead be complex numbers or components of a more abstract system, such a commutative ring. Analytic geometry is based on the usage of a coordinate system, which enables problems with geometry to be converted into problems with numbers and vice versa.

What is Coordinate Geometry

One of the most interesting ideas in mathematics is called coordinate geometry. By using graphs with curves and lines, coordinate geometry (also known as analytic geometry) explains how geometry and algebra are related. They can answer geometrical problems because it gives them geometrical aspects of algebra. In this area of geometry, a pair of ordered numbers is used to describe the location of points on a plane. Here, the fundamental ideas of coordinate geometry—also referred to as Cartesian geometry—as well as its formulas and their sources are discussed.

What do the terms coordinate and coordinate plane mean?

You must be comfortable using the numerical tables for both linear and nonlinear equations to plot graphs on a plane. The x-axis (horizontal line) and the y-axis (vertical axis) are two perpendicular axes that divide the number line, often referred to as a Cartesian plane, into four quadrants (vertical line).

The graph below shows the four quadrants together with their respective values.

• Quadrant 1: (+x, +y)
• Quadrant 2: (-x, +y)
• Quadrant 3: (-x, -y)
• Quadrant4: (+x, -y)

The characteristics of the point in the coordinate plane’s four quadrants are as follows:

• The origin O is the location where the x- and y-axes intersect, and its coordinates are (0, 0)
• The positive x-axis is to the right of the origin O, while the negative x-axis is to the left of the origin O. Additionally, the positive and negative y-axes are located above and below the origin O, respectively
• The first quadrant’s point (x, y) is plotted with reference to the positive x-axis and the positive y-axis because it has both positive values
• Plotting is done with reference to the negative x-axis and negative y-axis for the point depicted in the third quadrant (-x, -y).
• The positive x-axis and the negative y-axis are used to plot the point (x, -y) that is located in the fourth quadrant.

Definition of coordinate geometry

We can simply find any planet in the universe thanks to its coordinates. Longitudes and latitudes are two fictitious lines that make up the coordinate system of the Earth. We can locate any location on Earth using these coordinates.

Similar to this, we can find the point on a piece of paper or a plane by using coordinate axes like the x-axis and y-axis. We can calculate the lengths of lines and angles in a variety of methods. We can measure lines with rulers and angles with protractors. In coordinate geometry, measurements and other pertinent details about geometric figures can be discovered using graphs and coordinates.

Let’s begin by going through the characteristics of coordinate graphs. A rectangular grid with two axes of numbers is a coordinate graph. The horizontal number line is the x-axis, while the vertical number line is the y-axis. 

Geometry coordinate in Maths 

An address that aids in locating a spot in space is a coordinate. The coordinates of a point in a two-dimensional space are (x, y). Let’s note these two crucial terms right now.

• Abscissa: The distance from the origin along the x-axis is represented by the x value at the point (x, y).
• Ordinate: It is the y value at the coordinates (x, y) and the angle at which the point lies in relation to the x-axis, which runs parallel to the y-axis.

A point’s coordinates can be used for a variety of tasks, including calculating distance, midpoint, a line’s slope, and its equation.

Conclusion 

In this article we had come across from very basic definitions to complex concepts of coordinate geometry. We have seen the coordinate plane and its various related concepts. The article describes various quadrants of a coordinate plane and its application and it also deals with the abscissa and ordinate which together form coordinate geometry. Thus the article provides all the concepts related to coordinate geometry which will help to understand and solve questions more accurately.