What is a Cartesian Plane?
A Cartesian plane is a graph with two axes, one is called the x-axis and the other one is the y-axis. These two axes are perpendicular to each other. The origin (O) is in the exact center of the graph intersecting point of the two axes. Numbers to the right of the zero on the X-axis are positive and the numbers to the left of zero are negative. For the Y-axis, numbers below zero are negative and numbers above are positive.Let us study What is cartesian plane in detail.The Cartesian Plane is also referred to as the X-Y plane or the coordinate plane.
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Cartesian Plane Definition
A graph with two perpendicular number lines used to describe any point in the plane using an ordered pair of numbers is called a Cartesian Plane or the coordinate plane where one is vertically referred to as a Y axis and the other is horizontally referred to as the X axis and both form right angles with one another.
The Great Mathematician Rene Descartes' Latin name was Renatius Cartesius,who originally came up with the concept of a Cartesian plane named after him. Points on the cartesian plane are called ordered pairs written as (x , y).
The values that come first in ordered pairs are plotted along the horizontal line(x-axis) while the second number of ordered pairs is plotted along the vertical line(y-axis).
Cartesian Plane Quadrants
Take a plain sheet of paper, draw one horizontal line called X-axis and one vertical line called Y-axis such that it intersects at a point O. These two axes divide the cartesian plane into 4 parts each part is called a quadrant. A quadrant is ¼th part of a cartesian plane divided by coordinate axes.
There are four corners you need to know about on the graph.
First Quadrant = Top right.
Second Quadrant = Top left.
Third Quadrant = Bottom left.
Fourth Quadrant = Bottom right.
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In the first quadrant, both the coordinates are positive.
In the second quadrant, x-coordinate is negative whereas the y-coordinate is positive
In the third quadrant, both the coordinates are negative.
In the fourth quadrant, the x-coordinate is positive whereas the y-coordinate is negative.
The cartesian coordinate system includes a cartesian plane. This coordinate system has the ability to be translated into one, two, or three dimensions. The cartesian plane is the plane in two dimensions. It's also known as the coordinate plane. A cartesian plane is defined as a plane that is formed by the intersection of two perpendicular coordinate axes. While the y-axis is the vertical axis, the x-axis is the horizontal axis. The origin, whose location is represented as, is where these axes connect (0, 0). Any point on the cartesian plane can be represented as (x, y). The distance between the point and the y-axis is given by x, while the distance between the point and the x-axis is given by y.
Ordinate and Abscissa Definition
Ordered pairs are called the ordinate and abscissa on a Cartesian plane.
Abscissa
The distance of any point on the plane from the Y-axis is called the abscissa.The abscissa is the first number in an ordered pair. It is the x-value.
Ordinate
The distance of any point on the plane from the X-axis is said to be ordinate.
The ordinate is the second number in an ordered pair. It is the y-value
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Origin
The center point of intersection from which the distances are marked is called the origin. In a two- dimensional plane, the X-axis, and Y-axis intersect at a point called the origin.
The above graph shows four ordered pairs:
The first point (-3,1), -3 is the abscissa and 1 is the ordinate.
The second point (2,3), 2 is the abscissa and 3 is the ordinate.
The point (0,0), 0 is the abscissa and the ordinate.
For the point (-1.5,-2.5), -1.5 is the abscissa and -2.5 is the ordinate.
Don’t forget that the first point you get will always be on the X portion of the graph, and the second number will always be the Y.
One Dimensional Cartesian Plane
In one dimensional Cartesian Plane, draw a straight line and choose a point O as the origin in the center of the line. Then, write numbers, positive 1 to infinity to the right and negative 1 to infinity to the left. This line is also referred to as a number line. Here any point can have only single number position hence it is called as one-dimensional cartesian plane
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Two Dimensional Cartesian Plane
A two-dimensional plane that is formed by the intersection of one horizontal number line and one vertical number line, referred as x-axis and y-axis respectively, is called a two dimensional cartesian plane. These lines are perpendicular to each other and intersect at a point O called the origin. These axes divide the plane into four parts called quadrants. This plane is called the cartesian plane or coordinate plane or XY- plane.
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.
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Three Dimensional Cartesian Plane
The three-dimensional Cartesian plane has one more axis perpendicular to the normal Cartesian plane. There is a third axis, Z-axis , 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 defines the position along the X-axis, y defines the position along the Y-axis, and z defines the position along the Z-axis. The given graph shows the three dimensional Cartesian plane with three axes X, Y, and Z.
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How to plot points on a cartesian plane?
When graphing points on a cartesian plane, all distances are measured from the origin (0, 0). A signed ordered pair of points is used to symbolise the points. The steps below are used to plot a point on the cartesian plane, P(7, -6).
Check the x and y coordinates of the spot for signs. Determine which quadrant the point will be in based on the signals. The point P(7, -6) will be in the fourth quadrant since its signs are of the form (+, -).
Move x spaces to the left (negative) or right (positive) on the x-axis from the origin using the x coordinate value. From this point, draw a vertical perpendicular line. Because the point's x coordinate is 7, draw a vertical line 7 spaces to the right of the origin on the x-axis.
Move y spaces from the origin to the bottom (negative) or top (positive) of the y-axis using the y coordinate value. From this point, draw a horizontal perpendicular line. We move 6 spaces downhill from the origin since the y coordinate value is -6. We'll now draw a horizontal line.
Our point P is the intersection of these two lines (5, -6).
If there is a point to be made in the form of (0, y). It means that the location is y units away from the x-axis on the y-axis.
Assume that our point is defined by (x, 0). The point is then located on the x-axis, x distance from the y axis.
Solved Examples
Example 1: Plotting points (1,2) on a cartesian board.
Solution:
To plot a point, move along the x axis to find the first coordinate (the first number), then move up or down to find the second coordinate.
The first point you get will always be on the X portion of the graph, and the second number will always be the Y. For example, (1,2) means 1 space1 on the x-axis and 2 on the y-axis.
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Example 2: Plot A(2,-2) , B(-5,3), and C(-4,-6).
Solution:
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FAQs on Cartesian Plane
1. What is a cartesian coordinate system?
In a plane, a Cartesian coordinate system identifies each point uniquely by a pair of numerical coordinates, which are the signed distances from two fixed perpendicular oriented lines, measured in the same unit of length. Each reference line is known as a coordinate axis or simply axis of the system, and the place where they intersect is called the system's origin (0, 0). The coordinates may also be defined as the signed distances from the origin of the perpendicular projections of the point onto the two axes.
2. What are the parts of a cartesian plane?
There are three major parts to a cartesian plane. When trying to identify a point on the cartesian plane or build the graph of a function, these three pieces are crucial. The following is a list of the major parts of a cartesian plane:
Axes:
The axes are the two lines that intersect to produce the cartesian plane. The x-axis refers to the horizontal line. The y-axis is the vertical line that runs perpendicular to the x-axis.
Origin:
The origin is defined as the place where the two perpendicular axes x and y meet. The origin's coordinates are given by (0, 0). The origin divides the axes into two equal pieces.
Quadrants:
The cartesian plane is divided into four parts when the x and y axes intersect. These are referred to as quadrants, and they can go on indefinitely.
3. What are the cartesian plane quadrants?
The cartesian plane is divided into four infinite zones when the two axes intersect. Quadrants refer to these four areas. The two semi-x and y axes connect the quadrants. In an anti-clockwise manner, the quadrants can be numbered from one to four. In each coordinate, the x and y coordinates of a point will have different signs. A point can be placed in a specific quadrant based on its value, as seen below.
x > 0 and y > 0 in the first quadrant. As a result, a point's sign will be (+, +).
x <0 and y > 0 in the second quadrant. As a result, a point's sign will be (-, +).
x <0 and y<0 in the third quadrant. As a result, a point's sign will be ( -, -).
x > 0 and y <0 in the fourth quadrant. As a result, a point's sign will be (+, -).
Upwards and to the right will be the positive direction, while downwards and to the left will be the negative direction.
4. What are the Uses of Cartesian Planes?
Cartesian planes are used to plot the solutions to formulas with two variables, typically represented by x and y, though other symbols can be substituted for the x- and y-axis, so long as they are properly labeled and follow the same rules as x and y in the function.
These visual tools provide students with a pinpoint using these two points that account for the solution to the equation.
Students may also solve for a missing variable if x or y is unknown by simplifying the equation until both variables have a solution and can be plotted on a Cartesian plane. This process forms the basis for most early algebraic computations and data mapping.
