X and Y Axis are the foundation of the Cartesian coordinate system as well as graphs in mathematics. The x-axis and y-axis are crucial components of the coordinate plane, with the x-axis serving as a horizontal number line and the y-axis as a vertical number line. The x-axis is referred to as the abscissa, while the y-axis is known as the ordinate.
They intersect at right angles to create the coordinate plane. The point where the X and Y axis intersect is called the origin and is represented by the coordinates (0, 0) i.e. , the intersection of the X and Y axis.
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What is X-Axis?
The Horizontal line that divides the cartesian plane into two equal parts is called the x-axis various properties of the x-axis are,
- X axis is the horizontal line on a graph or coordinate plane.
- The X-axis is used to represent the variable(x) in the graph.
- Any point on the x-axis has 0 as its y-coordinate.
- The equation of the x-axis is, y = 0
Positive and Negative X-Axis
The X axis is a horizontal line that runs from left to right on the Cartesian plane. The right-hand side of the origin is considered the positive X axis (+X), while the left-hand side is the negative X axis (-X). The X axis divides the plane into two halves, known as quadrant
Points on X Axis
All points on the X axis have a Y-coordinate of zero since they lie on a horizontal line. These points are represented in the form of (x, 0), where x is the X-coordinate. Equation of X Axis
Equation of X-Axis
The equation of the X axis is simply y = 0, where y represents the Y-coordinate. This equation indicates that all the points on the X axis have a Y-coordinate of zero.
What is Y-Axis?
The Horizontal line that divides the cartesian plane into two equal parts is called the x-axis various properties of the x-axis are,
- Y axis is the vertical line on a graph or cartesian plane.
- It is used to represent the variable(y) in the graph.
- Any point on the y-axis has 0 as its x coordinate.
- Equation of y-axis is, x = 0
Positive and Negative Y-Axis
The Y axis extends upward from the origin, and all points on this axis have a positive Y-coordinate. Conversely, it extends downward, and points on this side have a negative Y-coordinate. The positive direction is usually denoted as the upward direction, and the negative direction is denoted as the downward direction.
Points on Y Axis
All points on the Y axis have an X-coordinate of zero since they lie on a vertical line. These points are represented in the form of (0, y), where y is the Y-coordinate.
Equation of Y Axis
The equation of the Y axis is simply x = 0, where x represents the X-coordinate. This equation indicates that all the points on the Y axis have an X-coordinate of zero.
Learn More: Coordinate Axes and Coordinate Planes in 3D.
X and Y Axis on Graph
When the X and Y axes are combined, they form a grid known as the Cartesian Plane or the XY plane. This plane is divided into four quadrants, each designated by Roman numerals I, II, III, and IV. Quadrant I is in the upper right, Quadrant II is in the upper left, Quadrant III is in the lower left, and Quadrant IV is in the lower right.
Plotting Points on X and Y Axis
To determine any point on the coordinate plane, we apply an ordered pair where the ordered pair is formulated as (x-coordinate, y-coordinate)/(x, y). Here the x-coordinate denotes a point on the x-axes which is the perpendicular distance from the y-axes and the y-coordinate denotes a point on the y-axes that is the perpendicular distance from the x-axes, therefore it is obvious from above that x-axis comes first when addressing the ordered pair to locate a point.
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Axis and Quadrants of Cartesian Plane
The X and Y axes divide the Cartesian Plane into four quadrants, each with unique characteristics.
- Quadrant I contain points with both positive X and Y coordinates.
- Quadrant II contains points with negative X and positive Y coordinates.
- Quadrant III contains points with negative X and Y coordinates.
- Quadrant IV contains points with positive X and negative Y coordinates.
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Solved Examples X and Y Axes
Problem 1: Plott the given points on the cartesian plane.
- A: (2, 3)
- B: (-1, 4)
- C: (0, -2)
- D: (-3, -4)
- E: (6, -5)
Solution:
Given Points,
- Point A: (2, 3)
- Point B: (-1, 4)
- Point C: (0, -2)
- Point D: (-3, -4)
- Point E: (6, -5)
To plot these points on the coordinate plane, start at the origin (0, 0) and move horizontally and vertically according to the X and Y values of each point.
- For Point A (2, 3), move two units to the right along the X-axis and three units upward along the Y-axis to locate the point.
- For Point B (-1, 4), move one unit to the left along the X-axis and four units upward along the Y-axis.
- For Point C (0, -2), stay at the origin and move two units downward along the Y-axis.
- Point D (-3, -4), move 3 units to the left along the X-axis and 4 units downwards along the Y-axis from the origin locate the point.
- Point E (6, -5), move 6 units to the right along the X-axis and 5 units downwards along the Y-axis from the origin locate the point.
Now, let’s graph these points on the coordinate plane. The resulting graph will show the positions of these points relative to the origin.
Problem 2: Plot a graph of the linear equation y = 2x + 1
Solution:
Given equation,
y = 2x + 1
To graph this linear equation, we need to find several points that satisfy the equation and then connect them to form a line. We can choose any X value and find the corresponding Y value using the equation.
Let’s calculate y for different values of x,
y = 2(0) + 1
y = 1
So, the point (0, 1) lies on the line.
y = 2(1) + 1
y = 3
So, the point (1, 3) lies on the line.
y = 2(-1) + 1
y = -1
So, the point (-1, -1) lies on the line.
Now, plot these points on the coordinate plane and connect them to form a straight line. The graph of the linear equation y = 2x + 1 will look like this:
X and Y Axis – FAQs
What are the Uses of the X-axis and Y-axis in Mathematics?
The X-axis and Y-axis are used to represent the horizontal and vertical number lines in the Cartesian coordinate system. They help locate points on a two-dimensional plane and are crucial for graphing functions and analyzing data.
How to Plot Points on Coordinate Plane?
To plot a point (X, Y), start at the origin (0, 0) and move horizontally X units along the X-axis and vertically Y units along the Y-axis to locate the point.
How to Plot a Linear Equation?
To plot a linear equation, find several points that satisfy the equation by choosing different X values and calculating the corresponding Y values. Plot these points on the coordinate plane and connect them with a straight line.
Can a Point lie on both X-axis and Y-axis at Same Time?
No, a point cannot lie on both the X-axis and Y-axis simultaneously. If a point lies on the X-axis, its Y-coordinate will be zero, and if it lies on the Y-axis, its X-coordinate will be zero.
What is Origin (0, 0) in Cartesian Coordinate System?
The origin is the point of intersection of the X-axis and Y-axis. It serves as the reference point for all coordinates on the plane, and its coordinates are (0, 0).
What are 4 Quadrants in Cartesian Coordinate System?
Four quadrants in cartesian coordinate system are,
- First Quadrant: X and Y coordinates are both positive (+, +)
- Second Quadrant: X coordinate is negative, Y coordinate is positive (-, +)
- Third Quadrant: X and Y coordinates are both negative (-, -)
- Fourth Quadrant: X coordinate is positive, Y coordinate is negative (+, -)
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