Find the Distance Between Two Points (0,-7) and (-6,1)

$(0, - 7)$ and $(- 6, 1)$

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.

$\sqrt{{((- 6) - 0)}^{2} + {(1 - (- 7))}^{2}}$

Step 3

Simplify.

Subtract $0$ from $- 6$ .

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

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

$\sqrt{36 + {(1 - (- 7))}^{2}}$

Multiply $- 1$ by $- 7$ .

$\sqrt{36 + {(1 + 7)}^{2}}$

Add $1$ and $7$ .

$\sqrt{36 + 8^{2}}$

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