Find the Distance Between Two Points (-1,2) and (-7,-6)

$(- 1, 2)$ and $(- 7, - 6)$

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.

$\sqrt{{((- 7) - (- 1))}^{2} + {((- 6) - 2)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 1$ .

$\sqrt{{(- 7 + 1)}^{2} + {((- 6) - 2)}^{2}}$

Add $- 7$ and $1$ .

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

Raise $- 6$ to the power of $2$ .

$\sqrt{36 + {((- 6) - 2)}^{2}}$

Subtract $2$ from $- 6$ .

$\sqrt{36 + {(- 8)}^{2}}$

Raise $- 8$ to the power of $2$ .

$\sqrt{36 + 64}$

Add $36$ and $64$ .

$\sqrt{100}$

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2}}$

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

$10$

Step 4