Find the Distance Between Two Points (2,3) , (6,9)

$(2, 3)$ , $(6, 9)$

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.

$\sqrt{{(6 - 2)}^{2} + {(9 - 3)}^{2}}$

Step 3

Simplify.

Subtract $2$ from $6$ .

$\sqrt{4^{2} + {(9 - 3)}^{2}}$

Raise $4$ to the power of $2$ .

$\sqrt{16 + {(9 - 3)}^{2}}$

Subtract $3$ from $9$ .

$\sqrt{16 + 6^{2}}$

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

$\sqrt{16 + 36}$

Add $16$ and $36$ .

$\sqrt{52}$

Rewrite $52$ as $2^{2} \cdot 13$ .

Factor $4$ out of $52$ .

$\sqrt{4 (13)}$

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

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

Pull terms out from under the radical.

$2 \sqrt{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{13}$

Decimal Form:

$7.21110255 \dots$

Step 5