Vertical Line: Properties, Formula and Examples

Vertical Lines in Coordinate Geometry: While trying to solve the problem of describing the position of a point on a plane, the French Mathematician René Descartes came up with the Cartesian coordinate system and the cartesian plane, from which we derive a vertical and horizontal line. To plot a point on a plane surface, two axes – vertical (y-axis) and horizontal (x-axis) lines are drawn on a plane. The line parallel to the y-axis is called the vertical line.

A vertical line means that it either goes from top to bottom or bottom to top. All points on this line will have the same x-coordinate. For instance, if a point on a vertical line is being mapped on a Cartesian plane, it can be denoted as (2,1), (5,1), or (-7,1) depending on the location on the y-axis. Let’s try to understand the vertical line by looking at its definition, properties, and solved examples.

Vertical Line: Definition

So, what is a vertical line? A Vertical line can be defined as a line on the coordinate plane where all points on the line have the same x-coordinate. You can understand this by looking at the vertical lines mapped on a coordinate plane here:

Vertical Line on a Coordinate Plane (Y-axis)

Vertical Lines and Horizontal Lines

The lines that are perpendicular to vertical lines and parallel to the x-axis are called horizontal lines. Vertical and Horizontal lines are essential for creating closed shapes and defining the position of objects in space. Additionally, these lines help measure the area, surface area, and volume of closed objects.

Vertical Lines: Plotting Points on a Coordinate Plane

A coordinate (or cartesian) plane is defined by two perpendicular lines – the vertical line (y-axis) and the horizontal lines (x-axis). A coordinate plane is made of squares, and each point represents a coordinate that can be expressed by x and y which indicate the horizontal and vertical position of the point. This simple concept has allowed the development of the Geographic coordinate system, which helps us share any location on the planet Earth with the help of longitude and latitude.

Coming to the simple coordinate plane, you can understand how a point can be plotted by looking at the image above. The point where the vertical line and the horizontal line intersect is called the origin, represented as (0,0). The point P on the plane is marked as (3,5) since it is 5 units from the horizontal line (x-axis) and 3 units from the vertical line (y-axis).

Vertical Line: Properties

The following list identifies and describes certain properties of vertical lines:

A vertical line is one that goes straight up and down, parallel to the y-axis of the coordinate plane.
A vertical line has no slope or it can be said that its slope is undefined.
To check whether the relation is a function in maths, we use a vertical line. It would be a function if all vertical lines intersect it a minimum of once. This is also called a vertical line test.

Vertical Line: Formulas

The equation of a vertical line is

x = a
where:
x is the x coordinate of any point on the line
a is where the line crosses the x-axis (x-intercept).

Example 1: Draw and plot the equation (x=6), and (y= -5).

Solution:

The point is marked on the plane as A (6,-5).

Example 2: Draw and plot the equation (x=25), and (y= 32).

Solution:

The point is marked on the plane as A (25,32).

Example 3: Plot A = (25,25)

Solution:

In this graph, A is a vertical line that passes through the x-axis at 25 units on the right side of the origin and is parallel to the y-axis.

Frequently Asked Questions About Vertical Lines

Following are the frequently asked question about vertical lines:

Question: What is a vertical line?
Answer: A vertical line can be defined as a line on the coordinate plane where all points on the line have the same x-coordinate.

Question: What way does the vertical line go?
Answer: In a coordinate plane, a vertical line is always straight from top to bottom.

Question: What are some common types of lines in Geometry?
Answer: Some of the most common lines in geometry are:
1) Vertical lines (that go up or down and are perpendicular to horizontal lines)
2) Horizontal lines (that go either left or right and are perpendicular to vertical lines)
3) Diagonal lines (that go straight in any direction except vertical or horizontal).

Question: What is a horizontal line?
Answer: A horizontal line is a straight line that is mapped from left to right and it is parallel to the X-axis in the plane coordinate system.

Question: What is the equation of a vertical line?
Answer: The equation of a vertical line is:
x = a
where:
x is the x coordinate of any point on the line
a is where the line crosses the x-axis (x-intercept).

Question: What is the difference between vertical and horizontal lines?
Answer: A vertical line is any straight line that goes up or down. A horizontal line is any line that goes left or right and is perpendicular to the vertical line.

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We hope this article on Vertical Lines was helpful. The concept of vertical lines will be useful in solving problems and plotting objects in coordinate geometry. If you have any queries regarding this article, do let us know about it in the comment section. We will get back to you at the earliest.

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