On this page, we practice finding the distance between two points in one dimension.
We practice:
- finding the distance between positive coordinates
- finding the distance when one coordinate is negative
- finding the distance between two negative coordinates
- working with fractions
- understanding when the distance is zero
Remember
Use the formula:
$$d=|P_2-P_1|$$
The absolute value makes the answer non-negative.
The order of the two points does not change the distance.
Example 1 – Two Positive Coordinates
Find the distance between:
$$P_1=3$$
and
$$P_2=9$$
Solution:
$$d=|9-3|$$
$$d=|6|$$
$$d=6$$
So, the distance is \(6\) units.
Example 2 – One Negative Coordinate
Find the distance between:
$$P_1=4$$
and
$$P_2=-2$$
Solution:
$$d=|-2-4|$$
$$d=|-6|$$
$$d=6$$
So, the distance is \(6\) units.
Example 3 – Two Negative Coordinates
Find the distance between:
$$P_1=-7$$
and
$$P_2=-3$$
Solution:
$$d=|-3-(-7)|$$
Subtracting a negative becomes addition:
$$d=|-3+7|$$
$$d=|4|$$
$$d=4$$
So, the distance is \(4\) units.
Example 4 – Fractional Coordinate
Find the distance between:
$$P_1=\frac{1}{2}$$
and
$$P_2=3$$
Solution:
$$d=\left|3-\frac{1}{2}\right|$$
$$d=\left|\frac{6}{2}-\frac{1}{2}\right|$$
$$d=\left|\frac{5}{2}\right|$$
$$d=\frac{5}{2}$$
As a decimal:
$$d=2.5$$
So, the distance is \(2.5\) units.
Example 5 – Distance between the Same Point
Find the distance between:
$$P_1=-4$$
and
$$P_2=-4$$
Solution:
$$d=|-4-(-4)|$$
$$d=|-4+4|$$
$$d=|0|$$
$$d=0$$
So, the distance is \(0\) units.
This happens because both points are at the same position.
Practice
- More Examples (Current page)
- Take the Quiz
Continue Learning
- Plotting Points on a Number Line (\(1D\))
- Distance Formula in \(1D\)
- Distance between Two Points in \(1D\)