Linear lines or straight lines are a basic element in geometry. This type of lines begin to study in elementary school. It is possible that you are at this very moment learning this concept or that your children are doing it. In this way you will solve your doubts about it and you will learn one more concept of basic geometry.
We hope you will find it interesting and that it will help you learn many more equally interesting things. If you’re ready to get started, keep reading!
What are Linear lines? Meaning
In geometry when we talk about linear lines we refer to straight lines. Straight lines are a basic element in this matter. Did you know that the term straight comes from the Latin rectus? The description of this word is simple. A line is considered to be those lines that lack curves or angles.
Straight lines are one-dimensional lines that also have neither beginning nor end. They are infinite and are also made up of infinite points that always advance in the same direction. In other words, this succession of points creates lines indefinitely.
Together with planes and points, they are fundamental elements within geometry. In case you didn’t know, geometry is the science that is responsible for studying both the measurements and the properties of any figure within a space or within a plane. Geometry is part of mathematics. But let’s continue with the lines.
There are many people who, when they begin to study lines, make mistakes and confuse them with segments. However it is not the same. Line segments are only a portion of a line. Since they are composed of an initial point and an end point. However, the lines, as we have explained a few lines above, are infinite, they always move towards the same direction and are composed of infinite points. This confusion is usually given by the way in which the concept is explained in schools.
Think that when the teacher tries to teach his students what a line is, what he does is draw a line segment on a piece of paper or on the blackboard. That is, a line with a beginning and an end. That is where the misunderstandings begin. The reality is that we can only draw line segments because they never end.
As for the straight lines, they can be divided into two types depending on their shape.
- Straight lines. Straight lines or linear lines have an indefinite shape and the points that make them up, also indefinite, always move in the same direction. Hence its shape is straight. If you looked at a straight line with a magnifying glass, you would realize that it is made up of thousands and thousands of tiny dots that, seen from afar, look like a single line.
- Curved lines. As for curved lines, they differ from straight lines in the direction taken by the points that make them up. While in straight or linear lines all points move in the same direction, the same is not the case with curved lines. In this case the points move in different directions or, at least, it does not have to always go in the same direction.
Types of linear lines in space
Linear lines occupy a position in space or on a plane. And depending on the position they have, they will receive a different denomination or another. In general terms, lines, or linear lines, can be, depending on their distribution in the plane or in space:
- Horizontal and vertical linear lines. If you want to learn a simple way to recognize horizontal lines without having to go crazy with theory, it is best to observe the world around you. The world around us is seen horizontally. Have you ever noticed that line that you see in the background when you look at the sea? It is the horizon line. Well, horizontal linear lines have the same shape. Horizontal lines form a right angle with vertical lines forming a perpendicular. If you think about the earth the vertical lines would go through the Earth. They would go from pole to pole. As in the image that you can see under these lines.
- Oblique linear lines. Now let’s go with the last concept. When a line is neither horizontal nor parallel in space, but has a different inclination, it is considered an oblique line. Likewise, if a straight line cuts another in a position without forming an angle of 90º, it is also called oblique.
Types of linear lines according to the position they acquire between them
Ok, we have now understood how lines are placed in space. And that depending on how they are placed, in addition to being linear lines, they will be horizontal, vertical or oblique. But we can go a little further. If there is a line that meets another, what type of lines are they based on their position between them? Well, we will talk about three basic types of linear lines depending on how they face each other. Do you want to meet them? Well, watch out:
- Parallel linear lines. We will say that two linear lines are parallel when they are equidistant from each other and always maintain the same inclination. In addition, both will go in the same direction. And both, as lines that they are, will be infinite. Parallel lines will never, ever cross their path. Can you think of some easy parallel lines to locate on Earth? Think about it calmly. Surely you have imagined the rails of a train! Indeed! The rails of a train are parallel to each other. If you’re ever not sure what the parallel lines are, always think about the rails.
- Perpendicular linear lines. Now think of two lines that intersect, and that, in doing so, generate 4 90º angles. If the angles that are created are right, we will be facing perpendicular linear lines. When we talk about the Earth, the horizon and the imaginary vertical line that goes from pole to pole, we conclude that both intersect each other becoming perpendicular lines.
- Intersecting linear lines. Now imagine that two lines intersect each other but do not create right angles. In that case, would they be perpendicular linear lines? No, you wouldn’t, they would be intersecting linear lines. They may not intersect but still face obliquely. In that case we would also consider them secants.
Some exercises with linear lines
Ok, we have already explained what linear lines are like and the different names they can acquire depending on how they are located on a plane or in space. Or depending on how they face each other. Would you like to do some exercises to see if you have understood well the different types of linear lines that you can find? In that case, read on. We have created a space in which we will show you a series of images so that you can find out what kind of linear lines they are. Below, if you are not sure or want to check your answers, you will find the solutions. Let’s get started!
Examples of Linear Lines
- Exercise 1. María has gone out for a walk with her boyfriend Juan. They both live near a river. They have decided to go to the shore to observe the water. However, many tokens of love have been found hanging on the railings on their way. Would you know what type of linear lines they are based on their position between them?
- Exercise 2. There is nothing more fun than watching a train. Maybe ride on it and be able to travel the length and breadth of the world. But the train has another very cool element. The rails. Through which the wagons and the locomotive circulate. These rails look like two linear lines facing each other that never touch. Do you know what position they have among them?
- Exercise 3. In the following image you can see three lines placed in different ways on the space. Would you know what types of linear lines are based on the relationship they occupy in space?
Solutions of linear lines
- Solution to exercise nº 1. It is clear that María and her boyfriend Juan are very much in love. And although we don’t know if they have hung their own lock as a token of their love or not, we do know that they are curious and notice the world around them. Hence they know that the lines on the railing where the locks rest are parallel to each other.
- Solution to exercise no. 2. Are you also in love with trains? Do you love stories of travel between cities? If so, the Murder on the Orient Express book may blow your mind. It is one of the most intriguing written by the queen of detective fiction, Agatha Christie. But let’s not deviate from the topic. Do you know what pattern the rails make? They are parallel linear lines. However, if you also look at the cut of the rails and the sleeper, the relationship between these lines is perpendicular.
- Solution to exercise no. 3. If you have paid attention to the image, you will have noticed that we have used it a few lines above with the solution to the problem. Line A is a linear line in a horizontal position. Line B is a linear line in a vertical position. And finally, line C is a linear line in an oblique position. Easy, right?