Find the Distance Between Two Points (1,3) , (3,7)

$(1, 3)$ , $(3, 7)$

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.

$\sqrt{{(3 - 1)}^{2} + {(7 - 3)}^{2}}$

Step 3

Simplify.

Subtract $1$ from $3$ .

$\sqrt{2^{2} + {(7 - 3)}^{2}}$

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

$\sqrt{4 + {(7 - 3)}^{2}}$

Subtract $3$ from $7$ .

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

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

$\sqrt{4 + 16}$

Add $4$ and $16$ .

$\sqrt{20}$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$\sqrt{4 (5)}$

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

$\sqrt{2^{2} \cdot 5}$

Pull terms out from under the radical.

$2 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{5}$

Decimal Form:

$4.47213595 \dots$

Step 5