Find the Distance Between Two Points (9,-9) , (-5,-10)

$(9, - 9)$ , $(- 5, - 10)$

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.

$\sqrt{{((- 5) - 9)}^{2} + {((- 10) - (- 9))}^{2}}$

Step 3

Simplify.

Subtract $9$ from $- 5$ .

$\sqrt{{(- 14)}^{2} + {((- 10) - (- 9))}^{2}}$

Raise $- 14$ to the power of $2$ .

$\sqrt{196 + {((- 10) - (- 9))}^{2}}$

Multiply $- 1$ by $- 9$ .

$\sqrt{196 + {(- 10 + 9)}^{2}}$

Add $- 10$ and $9$ .

$\sqrt{196 + {(- 1)}^{2}}$

Raise $- 1$ to the power of $2$ .

$\sqrt{196 + 1}$

Add $196$ and $1$ .

$\sqrt{197}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{197}$

Decimal Form:

$14.03566884 \dots$

Step 5