Explanation
In this lesson, we learn how to find the distance between two points in \(1D\).
\(1D\) means one-dimensional.
In \(1D\), points lie on a straight line, such as a number line.
For example:
\(\dots, −3, −2, −1, 0, 1, 2, 3, \dots\)
Each point on the number line represents a location.
If we have two points on a number line, such as:
\(P_1\) and \(P_2\)
then the distance between them tells us how far apart they are.
Distance is always positive.
For example, the distance from \(2\) to \(5\) is \(3\) units.
Also, the distance from \(5\) to \(2\) is still \(3\) units.
So, the order of the points does not change the distance.
Formula / Rule
The distance between two points in \(1D\) is:
\(d = \sqrt{(P_2 − P_1)^2}\)
where:
\(P_1\) is the first point
\(P_2\) is the second point
\(d\) is the distance between them
You may also see the formula written as:
\(d = \left| P_2 − P_1 \right|\)
Both formulas give the same answer.
We use:
\(d = \sqrt{(P_2 − P_1)^2}\)
because it connects clearly to the distance formulas in \(2D\) and \(3D\).
Example
Find the distance between:
\(P_1 = 2\) and \(P_2 = 5\)
Use the formula:
\(d = \sqrt{(P_2 − P_1)^2}\)
Substitute the values:
\(d = \sqrt{(5 − 2)^2}\)
Simplify:
\(d = \sqrt{3^2}\)
\(d = 3\)
So, the distance between \(2\) and \(5\) is:
\(3\) units
Video Explanation
Practice
Continue Learning
- Plotting Points on a Number Line (\(1D\))
- Distance Formula in \(1D\) (Current lesson)
- Distance between Two Points in \(1D\)