Lines: When we as humans started to make sense of the world around us, one of the earliest ways to do so was Geometry. Since Geo comes from Earth, and Metry implies measurement, Geometry is simply associated with measuring, plotting, and trying to understand the space, shapes, and things that we see and how they relate to each other.

One of the first things to start us off with Geometry is Lines. To measure the size or distance of any object, we use lines. In this article, we will study one of the core concepts of Geometry – Lines.

Lines: What Is A Line?

Definition of Line: Casey, 1893 defined a line as a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is sometimes called a straight line or, more archaically, a right line. To understand lines properly, let’s look at some of the rules that a line follows:

• It is a straight set of points that extends in opposite directions.
• It has no ends in both directions(infinite).
• It has no thickness.
• it is one-dimensional.

To further understand lines, let’s understand some basics of Geometry:

Basics of Geometry – Points, Line Segment, Ray, and Line

So let’s imagine a blank vacuum of space. Let’s make a dot on this blank space, and name the point ‘a’. So now we have an object on this blank canvas which we can denote as point ‘a’. We can have another point on it called point ‘b’ Since they are points, they do not connect each other.

Point

Geometrically, we can define a point as a location. It has no size i.e. no width, no length, and no depth. A point is shown by a dot. It has zero dimensions.

Line Segment

Now let’s take two other points and call them p and q, so if we connect p and q by starting from p and touch the point q, it is called a line segment. In this line segment, point p and q are called endpoints. Also, we can label or denote this line segment as PQ.

Rays

In the same space where we have the points a and b, as well as the line segment PQ, let’s make two points x and y, and connect them. But this time, it originates from x, touches y, and then keeps on going endlessly. Such a structure is called a ray. Since the origin of the ray is x, it will be called a vertex. A ray can be defined as a part of a line that has one endpoint (i.e. starting point) and it extends in one direction endlessly.

Lines

Finally, in this space, we have points ‘e’ and ‘f’ and we have an object that connected both the points ‘e’ and ‘f’ but keeps on going in both directions endlessly, this is known as a line. This line can be denoted as line EF.

Lines: Types Of Lines

When we study geometry, we will come across different types of lines. Let’s look at the 4 basic types of lines:

Horizontal Lines

When a line moves on a horizontal direction from left to right or vice versa it is called a horizontal line. In the below image, line XY is a horizontal line.

Vertical Lines

When a line moves on a vertical direction from top to bottom or bottom towards the top, it is called a vertical line. In the below image, the line PQ is a vertical line.

Parallel Lines

When two distinct lines are equidistant to each other and do not intersect at any point till infinity, they are called parallel lines. In the above image, lines EF and GH are parallel lines.

Perpendicular Lines

When two lines meet (intersect) each other at an angle of 90 degrees, they are called perpendicular lines. In the above image, lines AB and CD are parallel lines.

Lines: Angles

When two lines intersect each other, they form an angle. In Geometry, angles are defined as ” When two rays combine with a common endpoint, there forms an angle “. Accordingly, an angle is formed of two components: sides and vertex (the conjoined part).

These are the most basic type of angles found in Geometry:

1. Acute Angle
2. Obtuse Angle
3. Right Angle
4. Straight Angle
5. Reflex Angle
6. Full Rotation Angle (Considered in rare cases)

You can check out Types of Angles to know about angles in detail.

Lines: Intersecting And Non-Intersecting Lines

Intersecting Lines: When two or more lines meet at one common point, they are called intersecting lines. The point where all the lines converge is called the point of intersection.

There are some rules related to intersecting lines:

• The intersecting lines meet at one, and only one point, no matter at what angle they meet.
• No two straight lines can meet at more than one point.
• The lines that meet at more than one point are not straight lines. At least one of them is a curve.

Non-Intersecting Lines: When two or more lines never intersect each other, they are considered as non-intersecting lines. They are also called parallel lines. Another point to note is that they are equidistant from each other.

Lines: Straight Lines

Straight Lines: A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.

The general equation of a straight line is

y = mx + c,

where m is the gradient and (0,c) are the coordinates of the y-intercept.

We can find the equation of a straight line, given the gradient and a point on the line by using the formula:

y−b=m(x−a)

Where m is the gradient and (a,b) is on the line.

Frequently Asked Questions About Lines

Let’s look at some of the commonly asked questions about lines:

Question: What is a Line? Answer: In Geometry, a Line is a straight one-dimensional figure having no thickness and extending infinitely in both directions.

Question: What are Parallel Lines? Answer: When two distinct lines do not intersect at any point in infinity, they are called parallel lines.

Question: What is a line segment? Answer: An object connecting two dots on a plane is called a line segment.

Question: What are Perpendicular Lines? Answer: When two lines intersect each other at 90 degrees on the axis, they are called perpendicular lines.

Question: Who is the father of Geometry? Answer: Euclid is considered the Father of Geometry.

We hope you found all the information related to Lines helpful. To check your understanding of concept on Lines you can take up Mock Test on Lines and Angles. For any doubt on the content in this article feel to ask your doubt using comment box.

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