Different lines in math

May 4, 2022 | St. Peter's North

Lines are the building blocks of geometry. Lines are 2D objects, with no width, that can stretch on indefinitely, or join together with other lines to create shapes. There are many different lines to memorize and understand perpendicular, horizontal, etc. So below you can find a smorgasbord of all the different lines that make the shapes we know! 


Types of Lines

There are five types of lines. 


Vertical Line: A vertical line can be thought of as a standing line and has an undefined slope. We can draw a graph for a vertical line by plotting x = n, where n is equivalent to any sort of real number. All points in the vertical line have the same x coordinate and are parallel to the y-axis of the coordinate plane. 


You’ll see vertical lines in architectural pillars, the trunks of trees, the lines of a skyscraper, and so many other places!


Horizontal Line:

A horizontal line, also called a sleeping line, is a line in which all points have the same y - coordinate. It is parallel to the x-axis of the plane, and the slope of the horizontal line is zero. It is referred to as the sleeping line because it rules left to right without ever crossing the X-axis. Examples of horizontal lines include the ocean and the sky (the horizon), lines on a sheet of notebook paper, and the edge of a table.

The horizontal line equation is y = b. Here y is any point in the line of x coordinates, and b is the y-intercept. It is independent of x.


Parallel Line:

Two lines are parallel when the distance between the two straight lines is the same at all points. These two lines do not intercept or meet at any point. The symbol for parallel lines is ||, and you can find them in striped clothing, fence posts, or any other pair of lines.


Perpendicular Line:

Perpendicular lines are formed when a horizontal and a vertical line meet at a point. They are two lines that form a congruent adjacent angle with each other, clocking in at ninety degrees. The symbol for perpendicular lines is ⊥, and you’re most likely to see them on a grid or where lines come together to make a T shape. Clocks are the best examples of perpendicular lines at 3’O clock and 9’O clock. 


Other Geometric Lines

So far, we have learned about four different types of straight lines. However, there are even more types of lines that you’ll find in geometry!


intersecting lines - lines that meet at a point at any angle (unlike perpendicular lines, which only meet at 90°)

secant lines - lines that intersect a curve at two or more points

skew lines - lines that have no intersections with each other but are not equidistant (unlike parallel lines)

tangent lines - lines that touch a curve at one point


Line Segments and Rays

Some people get confused about the differences between lines, line segments and rays. Basically, the differences in their meanings are:

line - continues for infinity

line segment - has two endpoints

ray - has one endpoint; the other side continues for infinity

You can measure the length of a line segment, which is a part of a line, and all the points inside. You can’t measure a line or a ray, as they each have at least one side that continues without an endpoint. 


So, the line can be defined as a straight one-dimensional figure with no thickness and extends endlessly in both directions.

Lines are one of the important aspects and introduction to Geometry. With the types of lines introduced in this blog, kids will apply their ideas to real life and explore their thoughts.