# What is the distance between (2,6) and (4,4)?

Nov 26, 2015

$2 \sqrt{2}$

#### Explanation:

Consider these point as forming a triangle. You can then use Pythagoras to solve the length of the hypotenuse (the line between the points.

Let the distance be d

Let $\left({x}_{1} , {y}_{1}\right) \to \left(2 , 6\right)$
Let $\left({x}_{2} , {y}_{2}\right) \to \left(4 , 4\right)$

Then
$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

$d = \sqrt{{\left(4 - 2\right)}^{2} + {\left(4 - 6\right)}^{2}}$

$d = \sqrt{{2}^{2} + {\left(- 2\right)}^{2}}$

$d = \sqrt{8} = \sqrt{2 \times {2}^{2}}$

$d = 2 \sqrt{2}$

By keeping the square root you have an exact solution.
If you tried using decimal it would not be!