Find the Distance Between Two Points (1,3) , (3,9)

$(1, 3)$ , $(3, 9)$

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.

$\sqrt{{(3 - 1)}^{2} + {(9 - 3)}^{2}}$

Step 3

Simplify.

Subtract $1$ from $3$ .

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

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

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

Subtract $3$ from $9$ .

$\sqrt{4 + 6^{2}}$

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

$\sqrt{4 + 36}$

Add $4$ and $36$ .

$\sqrt{40}$

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$\sqrt{4 (10)}$

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

$\sqrt{2^{2} \cdot 10}$

Pull terms out from under the radical.

$2 \sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{10}$

Decimal Form:

$6.32455532 \dots$

Step 5