Find the Distance Between Two Points (-1,-2) and (5,2)

$(- 1, - 2)$ and $(5, 2)$

Step 1

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

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

Step 2

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

$\sqrt{{(5 - (- 1))}^{2} + {(2 - (- 2))}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 1$ .

$\sqrt{{(5 + 1)}^{2} + {(2 - (- 2))}^{2}}$

Add $5$ and $1$ .

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

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

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

Multiply $- 1$ by $- 2$ .

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

Add $2$ and $2$ .

$\sqrt{36 + 4^{2}}$

Raise $4$ to the power of $2$ .

$\sqrt{36 + 16}$

Add $36$ and $16$ .

$\sqrt{52}$

Rewrite $52$ as $2^{2} \cdot 13$ .

Factor $4$ out of $52$ .

$\sqrt{4 (13)}$

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

$\sqrt{2^{2} \cdot 13}$

Pull terms out from under the radical.

$2 \sqrt{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{13}$

Decimal Form:

$7.21110255 \dots$

Step 5