Find the Distance Between Two Points (0,-7) , (-2,5)

$(0, - 7)$ , $(- 2, 5)$

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.

$\sqrt{{((- 2) - 0)}^{2} + {(5 - (- 7))}^{2}}$

Step 3

Simplify.

Subtract $0$ from $- 2$ .

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

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

$\sqrt{4 + {(5 - (- 7))}^{2}}$

Multiply $- 1$ by $- 7$ .

$\sqrt{4 + {(5 + 7)}^{2}}$

Add $5$ and $7$ .

$\sqrt{4 + 12^{2}}$

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

$\sqrt{4 + 144}$

Add $4$ and $144$ .

$\sqrt{148}$

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.

$2 \sqrt{37}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{37}$

Decimal Form:

$12.16552506 \dots$

Step 5