Find the Distance Between Two Points (12,18) , (50,42)

$(12, 18)$ , $(50, 42)$

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Substitute the actual values of the points into the distance formula.

$\sqrt{{(50 - 12)}^{2} + {(42 - 18)}^{2}}$

Simplify.

Subtract $12$ from $50$ .

$\sqrt{38^{2} + {(42 - 18)}^{2}}$

Raise $38$ to the power of $2$ .

$\sqrt{1444 + {(42 - 18)}^{2}}$

Subtract $18$ from $42$ .

$\sqrt{1444 + 24^{2}}$

Raise $24$ to the power of $2$ .

$\sqrt{1444 + 576}$

Add $1444$ and $576$ .

$\sqrt{2020}$

Rewrite $2020$ as $2^{2} \cdot 505$ .

Factor $4$ out of $2020$ .

$\sqrt{4 (505)}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 505}$

Pull terms out from under the radical.

$2 \sqrt{505}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{505}$

Decimal Form:

$44.94441010 \dots$