Find the Distance Between Two Points (-2,-9) and (7,3)

$(- 2, - 9)$ and $(7, 3)$

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.

$\sqrt{{(7 - (- 2))}^{2} + {(3 - (- 9))}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 2$ .

$\sqrt{{(7 + 2)}^{2} + {(3 - (- 9))}^{2}}$

Add $7$ and $2$ .

$\sqrt{9^{2} + {(3 - (- 9))}^{2}}$

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

$\sqrt{81 + {(3 - (- 9))}^{2}}$

Multiply $- 1$ by $- 9$ .

$\sqrt{81 + {(3 + 9)}^{2}}$

Add $3$ and $9$ .

$\sqrt{81 + 12^{2}}$

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

$\sqrt{81 + 144}$

Add $81$ and $144$ .

$\sqrt{225}$

Rewrite $225$ as $15^{2}$ .

$\sqrt{15^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$15$

Step 4