Horizontal Line: Definition, Symmetry, Solved Examples

Horizontal Line is a widely used term in Maths and also in our day-to-day life. In coordinate geometry, a line is said to be horizontal if two points on the line have the same Y-coordinates. In simple terms, the straight line parallel to the horizon is called a horizontal line. Horizontal lines are also called sleeping lines.

On the X-Y axis, a horizontal line will always be parallel to the X-axis and perpendicular to the Y-axis. The word horizontal is derived from the word horizon. In this article, you can find all about horizontal lines, examples, equation, and facts. Read on to find out!

What is Horizontal Lines?

Horizontal lines in coordinate geometry are lines that are parallel to the X-axis. In other words, a line having points on the same Y-coordinate points is called a horizontal line. This means that the line that does not touch any point on the X-axis.

Horizontal lines are defined as lines that are parallel to the X-axis. In geometry, we can define a horizontal line in the form of an equation. The equation of a horizontal line is represented as y = constant. It is important to note that the slope of a horizontal line is always zero. Vertical lines are defined as the lines parallel to Y-axis. The vertical line is perpendicular to the horizontal line. Furthermore, the horizontal line is parallel to the horizon.

Horizon Analogy to Understand Horizontal Line

Horizon is a line along which the earth and sky seem to meet. The word horizontal is derived from the word horizon. Thus, in simple terms, the line parallel to the horizon is termed as a horizontal line.

How to Draw a Horizontal Line?

In order to draw a horizontal line using a graph, follow the steps provided below:

• To start with, define the X-axis and Y-axis and mark the numbers.
• Choose different points with different x coordinates but same y coordinate.
• Join all the points and extend it on both sides to get the horizontal line

Horizontal Line Equation

In geometry, we can represent a horizontal line in the form of an equation. Let us form an equation for the horizontal line passing through the point (0,2) as shown below:

We know that a straight line is represented as y = mx + C

For the point (0, 2), the equation will be:
y= (0) x+C
y = C
The line cuts the y-axis at (0, 2), thus, the value of C=2.
Therefore, y = 2.
Therefore, the equation of the horizontal line is y = 2.

Note that, in the above graph, even for other points on such as (-3, 2), (3, 2) or (-6, 2), (6, 2) or any other points, the y-coordinates will always be 2. In this situation, the line will be a horizontal line.

Uses of Horizontal Line: Horizontal Line of Symmetry

A horizontal line can help to visualise whether or not a figure or 3D object is symmetrical. In order to check the symmetry, visualise a horizontal line passing through the axis of the figure and object such that when folded on the horizontal line, both the equal pieces overlap.

Horizontal and Vertical Lines

Horizontal lines are the lines parallel to the x-axis and the y-intercept is always the same for all points on the line. Whereas, vertical lines are the lines parallel to y-axis and the x-intercept will be the same. Check the pictorial representation of horizontal and vertical lines from below:

Solved Examples on Horizontal Line

Let us go through some solved examples on horizontal lines:

Example 1: Check how many of the alphabets are horizontally symmetrical from the image given below:

Solution: We have drawn a horizontal line across the letters to decide if the letters are symmetrical. The alphabet ‘A’ is not horizontally symmetrical, but it is vertically symmetrical. Whereas, the alphabets, ‘B’, ‘C’ and ‘D’ are horizontally symmetrical.

Example 2: Check which equation is for a horizontal line from the graph given below:

Solution: The given equations of lines are as follows:

• y = x² – 5 
• y = x²
• y = x
• y = 3
• x = 3

In the above-mentioned equations, the line which has the same y-intercept on all points of the line is y=3. For the line y=3, the x-intercept varies while the y-intercept remains constant. Therefore, y=3 is a horizontal line.

Frequently Asked Questions on Horizontal Lines

Students might have a lot of questions related to horizontal lines. Here we have listed some of the frequently asked questions for reference:

Q.1. What is the rule for a horizontal line?
A. The horizontal line has the following properties:
– The line is parallel to the X-axis of the coordinate plane.
– The slope of a horizontal line is zero
– The y-intercept of a horizontal line is constant.

Q.2. How to draw a horizontal line?
A. To draw a horizontal line, the Y-coordinates must be constant and the X-coordinates can vary. Make multiple points with constant Y-coordinates and draw a line joining them.

Q.3. What is horizontal and vertical lines?
A. A horizontal line parallel to the X-axis. Whereas a vertical line is parallel to the Y-axis.

Q.4. Does a horizontal line have a slope?
A. No, the horizontal line does not have a slope.

Q. Which is an equation of a horizontal line?
A. The equation of a horizontal line will be: y = constant. The constant will be as per the Y-coordinate.

Q. What are the horizontal lines on the globe called?
A. The horizontal lines on the globe is called Latitude.

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