# What is the distance between (3,5) and (6,2)?

May 13, 2018

I tried this:

#### Explanation:

Here you can use for the distance $d$ the following expression (derived from Pythagoras Theorem):

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

using the coordinates of your points:

$d = \sqrt{{\left(6 - 3\right)}^{2} + {\left(2 - 5\right)}^{2}} = \sqrt{9 + 9} = \sqrt{18} = 4.2$ units

May 13, 2018

$d = 4.24$

#### Explanation:

d = sqrt((X_2 - X_1)^2 + (Y_2 - Y_1)^2

Coordinates are always in $\left(X , Y\right)$

So in $\left(3 , 5\right)$, we'll make our $3$ the ${X}_{2}$
So the $5$ is the ${Y}_{2}$

This means that in $\left(6 , 2\right)$, the $6$ is the ${X}_{1}$
And the $2$ is the ${Y}_{1}$

Now we plug our $X$ and $Y$ into the equation

d = sqrt((3 - 6)^2 + (5 - 2)^2

d = sqrt(( -3)^2 + ( 3)^2

$d = \sqrt{9 + 9}$

$d = \sqrt{18}$ $\approx$ $4.24$