Find the Distance Between Two Points (-1,-5) and (4,7)

$(- 1, - 5)$ 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.

$\sqrt{{(4 - (- 1))}^{2} + {(7 - (- 5))}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 1$ .

$\sqrt{{(4 + 1)}^{2} + {(7 - (- 5))}^{2}}$

Add $4$ and $1$ .

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

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

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

Multiply $- 1$ by $- 5$ .

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

Add $7$ and $5$ .

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

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