Find the Distance Between Two Points (-10,7) and (2,5)

$(- 10, 7)$ and $(2, 5)$

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.

$\sqrt{{(2 - (- 10))}^{2} + {(5 - 7)}^{2}}$

Simplify.

Multiply $- 1$ by $- 10$ .

$\sqrt{{(2 + 10)}^{2} + {(5 - 7)}^{2}}$

Add $2$ and $10$ .

$\sqrt{12^{2} + {(5 - 7)}^{2}}$

Raise $12$ to the power of $2$ .

$\sqrt{144 + {(5 - 7)}^{2}}$

Subtract $7$ from $5$ .

$\sqrt{144 + {(- 2)}^{2}}$

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

$\sqrt{144 + 4}$

Add $144$ and $4$ .

$\sqrt{148}$

Rewrite $148$ as $2^{2} \cdot 37$ .

Factor $4$ out of $148$ .

$\sqrt{4 (37)}$

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

$\sqrt{2^{2} \cdot 37}$

Pull terms out from under the radical.

$2 \sqrt{37}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{37}$

Decimal Form:

$12.16552506 \dots$