Find the Distance Between Two Points (4,-9) and (-5,3)

$(4, - 9)$ and $(- 5, 3)$

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.

$\sqrt{{((- 5) - 4)}^{2} + {(3 - (- 9))}^{2}}$

Step 3

Simplify.

Subtract $4$ from $- 5$ .

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

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