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

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

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.

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

Step 3

Simplify.

Subtract $0$ from $7$ .

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

Raise $7$ to the power of $2$ .

$\sqrt{49 + {(1 - (- 6))}^{2}}$

Multiply $- 1$ by $- 6$ .

$\sqrt{49 + {(1 + 6)}^{2}}$

Add $1$ and $6$ .

$\sqrt{49 + 7^{2}}$

Raise $7$ to the power of $2$ .

$\sqrt{49 + 49}$

Add $49$ and $49$ .

$\sqrt{98}$

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$\sqrt{49 (2)}$

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} \cdot 2}$

Pull terms out from under the radical.

$7 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{2}$

Decimal Form:

$9.89949493 \dots$

Step 5