Find the Distance Between Two Points (5,-1) , (-5,5)

$(5, - 1)$ , $(- 5, 5)$

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.

$\sqrt{{((- 5) - 5)}^{2} + {(5 - (- 1))}^{2}}$

Step 3

Simplify.

Subtract $5$ from $- 5$ .

$\sqrt{{(- 10)}^{2} + {(5 - (- 1))}^{2}}$

Raise $- 10$ to the power of $2$ .

$\sqrt{100 + {(5 - (- 1))}^{2}}$

Multiply $- 1$ by $- 1$ .

$\sqrt{100 + {(5 + 1)}^{2}}$

Add $5$ and $1$ .

$\sqrt{100 + 6^{2}}$

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

$\sqrt{100 + 36}$

Add $100$ and $36$ .

$\sqrt{136}$

Rewrite $136$ as $2^{2} \cdot 34$ .

Factor $4$ out of $136$ .

$\sqrt{4 (34)}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 34}$

Pull terms out from under the radical.

$2 \sqrt{34}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{34}$

Decimal Form:

$11.66190378 \dots$

Step 5