Find the Distance Between Two Points (5,-4) and (0,8)

$(5, - 4)$ and $(0, 8)$

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.

$\sqrt{{(0 - 5)}^{2} + {(8 - (- 4))}^{2}}$

Step 3

Simplify.

Subtract $5$ from $0$ .

$\sqrt{{(- 5)}^{2} + {(8 - (- 4))}^{2}}$

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

$\sqrt{25 + {(8 - (- 4))}^{2}}$

Multiply $- 1$ by $- 4$ .

$\sqrt{25 + {(8 + 4)}^{2}}$

Add $8$ and $4$ .

$\sqrt{25 + 12^{2}}$

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