The Cartesian plane describes the position of a point or the object on the surface by using the two intersecting lines. There are some other coordinate systems such as the polar coordinate system, spherical coordinate system, and cylindrical coordinate system. Let us discuss the different types of the Cartesian plane in detail.
Cartesian Plane Definition
The Cartesian plane consists of two directed and perpendicular lines whose intersection point is the zero point for both the lines. The horizontal line is known as X-axis, and the vertical line is known as Y-axis. The coordinate point (x, y) on the Cartesian plane says that the horizontal distance of the point from the origin is x, and the vertical distance is y.
If the sign of x is positive, the point is on the right of the origin; else it is on the left. Similarly, if the sign is positive for y, the point is y points above the origin else it is y points below it.
Cartesian Plane Quadrants
The X-axis and Y-axis split the plane into four parts, and they are called quadrants. Quadrants are denoted as I, II, III, and IV in an anticlockwise direction. The axes in the plane are called Cartesian axes, and the plane is known as the Cartesian plane.
Take, the ray
OX = Positive x-axis,
OX’ = Negative x-axis
OY = Positive y-axis
OY’ = Negative y-axis.
Thus the quadrants are characterized by the following signs of abscissa and ordinate:
- Quadrant x > 0 , y > 0 or (+,+)
- Quadrant x < 0 , y > 0 or (-,+)
- Quadrant x < 0 , y < 0 or ( -,-)
- Quadrant x > 0 , y < 0 or (+,-)
One Dimensional Cartesian Plane
For the Cartesian coordinate system in one dimension, draw a straight line and choose a point O as the origin in the middle of the line. The line segment, which is in the right of the origin O is positive, whereas the line segment in the left of the origin is negative. So give the sign as ‘+’ and ‘-’ to any point as we locate it on the number line. The line, which is chosen for determining the points in one dimension, is called the number line.
Origin:
The centre point from which the distances are marked is called the origin. In two- dimensional plane, the X-axis, and Y-axis crossed the point is called the origin.
Two Dimensional Cartesian Plane
The 2D Cartesian coordinate system is represented by the X-Y plane. The two mutually perpendicular lines represent the X-Y plane. The points are defined as the ordered pair and written in the parenthesis. It has two perpendicular lines. One of the lines is called the X-axis, and the other is Y-axis. The X-axis is the horizontal line, and Y-axis is the vertical line. The point where the two axes meet is called the origin O. For any given point P, let x and y be the corresponding number lines and the coordinates are written as (x, y).
Where x is called the abscissa, and y is called the ordinate.
Three Dimensional Cartesian Plane
The 3D Cartesian plane has one more axis perpendicular to the normal Cartesian plane. For the XY plane, there is an axis Z which is perpendicular to the XY plane. Any point lying on this plane is defined by the set of three points (x, y, z). Here, x represents the position along the X-axis, y defines the position along the Y-axis, and z denotes the position along the Z-axis. The given graph shows the 3D Cartesian plane with three axes X, Y, and Z.
Cartesian Representation of Complex Numbers
A complex number is a blend of real and imaginary numbers. We know that an imaginary number cannot be represented on a number line or Cartesian plane. Hence, they are represented on a complex plane. A complex plane is just like any other two-dimensional Cartesian plane. But here one axis will represent the real part of the number and the other axis will represent the imaginary part of the number. For a complex number a + ib, the point represented on the complex plane will be (a, b).
For example: Take a number 2 + 5i. The given graph will be as given here.
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Coordinate System | Vertical Line |
Complex Numbers | Real Numbers |