Find the Distance Between Two Points (5,2) , (11,-7)

$(5, 2)$ , $(11, - 7)$

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.

$\sqrt{{(11 - 5)}^{2} + {((- 7) - 2)}^{2}}$

Step 3

Simplify.

Subtract $5$ from $11$ .

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

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

$\sqrt{36 + {((- 7) - 2)}^{2}}$

Subtract $2$ from $- 7$ .

$\sqrt{36 + {(- 9)}^{2}}$

Raise $- 9$ to the power of $2$ .

$\sqrt{36 + 81}$

Add $36$ and $81$ .

$\sqrt{117}$

Rewrite $117$ as $3^{2} \cdot 13$ .

Factor $9$ out of $117$ .

$\sqrt{9 (13)}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 13}$

Pull terms out from under the radical.

$3 \sqrt{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{13}$

Decimal Form:

$10.81665382 \dots$

Step 5