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

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

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