Find the Distance Between Two Points (-4,5) , (2,3)

$(- 4, 5)$ , $(2, 3)$

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.

$\sqrt{{(2 - (- 4))}^{2} + {(3 - 5)}^{2}}$

Simplify.

Multiply $- 1$ by $- 4$ .

$\sqrt{{(2 + 4)}^{2} + {(3 - 5)}^{2}}$

Add $2$ and $4$ .

$\sqrt{6^{2} + {(3 - 5)}^{2}}$

Raise $6$ to the power of $2$ .

$\sqrt{36 + {(3 - 5)}^{2}}$

Subtract $5$ from $3$ .

$\sqrt{36 + {(- 2)}^{2}}$

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

$\sqrt{36 + 4}$

Add $36$ and $4$ .

$\sqrt{40}$

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$\sqrt{4 (10)}$

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

$\sqrt{2^{2} \cdot 10}$

Pull terms out from under the radical.

$2 \sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{10}$

Decimal Form:

$6.32455532 \dots$