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

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

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.

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

Step 3

Simplify.

Multiply $- 1$ by $- 5$ .

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

Add $0$ and $5$ .

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

Raise $5$ to the power of $2$ .

$\sqrt{25 + {(7 - (- 2))}^{2}}$

Multiply $- 1$ by $- 2$ .

$\sqrt{25 + {(7 + 2)}^{2}}$

Add $7$ and $2$ .

$\sqrt{25 + 9^{2}}$

Raise $9$ to the power of $2$ .

$\sqrt{25 + 81}$

Add $25$ and $81$ .

$\sqrt{106}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{106}$

Decimal Form:

$10.29563014 \dots$

Step 5