Find the Distance Between Two Points (-1,-9) , (6,6)

$(- 1, - 9)$ , $(6, 6)$

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.

$\sqrt{{(6 - (- 1))}^{2} + {(6 - (- 9))}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 1$ .

$\sqrt{{(6 + 1)}^{2} + {(6 - (- 9))}^{2}}$

Add $6$ and $1$ .

$\sqrt{7^{2} + {(6 - (- 9))}^{2}}$

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

$\sqrt{49 + {(6 - (- 9))}^{2}}$

Multiply $- 1$ by $- 9$ .

$\sqrt{49 + {(6 + 9)}^{2}}$

Add $6$ and $9$ .

$\sqrt{49 + 15^{2}}$

Raise $15$ to the power of $2$ .

$\sqrt{49 + 225}$

Add $49$ and $225$ .

$\sqrt{274}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{274}$

Decimal Form:

$16.55294535 \dots$

Step 5