# Distance between two points

In this article we review calculating the distance between two points, when coordinates of these points are known.

Distance between two plane points $A(x_1;y_1)$ and $B(x_2;y_2)$ can be calculated with this formula: $${AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}$$

## Solved examples

### Example No. 1

What is the distance between two plane points $A(5;10)$ and $B(20;30)$?

Using the formula above, we get:

$${AB=\sqrt{(20-5)^2+(30-10)^2}=25}$$Answer: AB = 25

### Example No. 2

What is the missing coordinate $A(x;7)$ value x, if we have other point $B(2;3)$ and the length of segment $AB$ is 5?

Using the formula above, we get this equation:

$${\sqrt{(2-x)^2+(3-7)^2}=5}$$To solve this equation, we take a square above sides of the equation, then simplify everything and solve equation by factoring:

$$\begin{align} \Bigl(\sqrt{(2-x)^2+(3-7)^2}\Bigr)^2 & =5^2 \\ (2-x)^2+16 & =25 \\ 4-4x+x^2+16 & =25 \\ x^2-4x-5 & =0 \\ (x-5)(x+1) & =0 \\ x=5 & \ \text{or} \ x=-1 \\ \end{align}$$Answer: x = 5 or x = -1

2019-03-02

### Comments

This article hasn't been commented yet.

### New articles

- Test quiz
- Exact values of trigonometric functions
- Signs of trigonometric functions
- Lower and upper quartiles of the data set. Interquartile range
- Mean, mode, median and range of the data set
- Probability of independent events
- Table of basic indefinite functions integrals
- Basic formulas and rules of calculating derivatives

## Write a comment