Find the Distance Between Two Points (6,5) and (-3,-7)

$(6, 5)$ and $(- 3, - 7)$

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.

$\sqrt{{((- 3) - 6)}^{2} + {((- 7) - 5)}^{2}}$

Step 3

Simplify.

Subtract $6$ from $- 3$ .

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

Raise $- 9$ to the power of $2$ .

$\sqrt{81 + {((- 7) - 5)}^{2}}$

Subtract $5$ from $- 7$ .

$\sqrt{81 + {(- 12)}^{2}}$

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