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

$(4, - 7)$ and $(- 1, 5)$

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Substitute the actual values of the points into the distance formula.

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

Simplify.

Subtract $4$ from $- 1$ .

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

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

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

Multiply $- 1$ by $- 7$ .

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

Add $5$ and $7$ .

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

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.

$13$