Explanation
In one dimension, points lie along a straight line called a number line.
Each point can be located using just one value.
For example, a point might be located at:
$$-3,\quad 0,\quad 2,\quad 5$$
If we know the positions of two points, \(P_1\) and \(P_2\), we can find the distance between them by taking the absolute value of their difference.
The absolute value makes sure that the distance is never negative.
A number line is usually drawn horizontally, but it can also be vertical or diagonal. The direction of the number line does not change the distance between the points.
Formula / Rule
The distance between two points \(P_1\) and \(P_2\) in \(1D\) is:
$$d=|P_2-P_1|$$
Where:
- \(d\) is the distance between the two points.
- \(P_1\) is the position of the first point.
- \(P_2\) is the position of the second point.
The formula can also be written as:
$$d=\sqrt{(P_2-P_1)^2}$$
Both formulas give the same distance.
Remember:
- Distance is always non-negative.
- If the two points are different, the distance is positive.
- If the two points are at the same position, the distance is \(0\).
- The order of the points does not matter because:
$$|P_2-P_1|=|P_1-P_2|$$
Example
Find the distance between:
$$P_1=1$$
and
$$P_2=5$$
Step 1: Use the formula.
$$d=|P_2-P_1|$$
Step 2: Substitute the values.
$$d=|5-1|$$
Step 3: Simplify.
$$d=|4|$$
$$d=4$$
So, the distance between the two points is \(4\) units.
On a number line, moving from \(1\) to \(5\) covers a distance of \(4\) units.
Video Explanation
Practice
Continue Learning
- Plotting Points on a Number Line (\(1D\))
- Distance Formula in \(1D\)
- Distance between Two Points in \(1D\) (Current lesson)