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

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

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.

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

Simplify.

Subtract $0$ from $7$ .

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

Raise $7$ to the power of $2$ .

$\sqrt{49 + {(2 - (- 5))}^{2}}$

Multiply $- 1$ by $- 5$ .

$\sqrt{49 + {(2 + 5)}^{2}}$

Add $2$ and $5$ .

$\sqrt{49 + 7^{2}}$

Raise $7$ to the power of $2$ .

$\sqrt{49 + 49}$

Add $49$ and $49$ .

$\sqrt{98}$

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$\sqrt{49 (2)}$

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} \cdot 2}$

Pull terms out from under the radical.

$7 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{2}$

Decimal Form:

$9.89949493 \dots$