Find the Distance Between Two Points (9,5) and (4,-7)

$(9, 5)$ and $(4, - 7)$

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.

$\sqrt{{(4 - 9)}^{2} + {((- 7) - 5)}^{2}}$

Step 3

Simplify.

Subtract $9$ from $4$ .

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

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

$\sqrt{25 + {((- 7) - 5)}^{2}}$

Subtract $5$ from $- 7$ .

$\sqrt{25 + {(- 12)}^{2}}$

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

$\sqrt{25 + 144}$

Add $25$ and $144$ .

$\sqrt{169}$

Rewrite $169$ as $13^{2}$ .

$\sqrt{13^{2}}$

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

$13$

Step 4