In these lessons, we will learn

- how to derive the distance formula from the Pythagorean Theorem.
- how to use the distance formula.

We also have a distance formula calculator that can calculate the distance between two points. Use it to check your answers.

Related Topics:

More Geometry Lessons

More Algebra Lessons

In the coordinate plane, we can use the distance formula to find the distance between any two points. The distance formula can be derive from the Pythagorean Theorem.

The distance between the two points (x_{1},y_{1}) and
(x_{2},y_{2}) is given by the distance formula.

*Example:*

To find the distance between the points *P*(2, 3) and *Q*(1, 1). We can sketch the right-angled triangle *PQR* with *PQ* as the hypotenuse.

**Solution:**

Using Pythagoras theorem: *PQ*^{2} = (2 – 1)^{2} + (3 –1)^{2}

⇒ *PQ *=

In general, the distance between two points *P*(*x*_{1},*y*_{1}) and *Q*(*x*_{2},*y*_{2}) is given by the **distance formula**:

*Example:*

Find the distance between the points *A*(1, 2) and *B*(-3, -2).

**Solution:**

Using the distance formula:

Distance =

= 5.66 (correct to 2 decimal places)

Worksheet 1, Worksheet 2 to calculate the distance between two points.

This video shows how the distance formula comes from the Pythagorean Theorem, and do one simple example of finding the distance between two points.

The following videos show the Distance Formula and how to find the Distance Between Two Points.

The following video gives another example of using the distance formula.

This distance formula calculator can calculate the distance between two given points on the coordinate plane.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.