Find the Distance Between Two Points (3,7) and (6,5)

$(3, 7)$ and $(6, 5)$

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.

$\sqrt{{(6 - 3)}^{2} + {(5 - 7)}^{2}}$

Step 3

Simplify.

Subtract $3$ from $6$ .

$\sqrt{3^{2} + {(5 - 7)}^{2}}$

Raise $3$ to the power of $2$ .

$\sqrt{9 + {(5 - 7)}^{2}}$

Subtract $7$ from $5$ .

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

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

$\sqrt{9 + 4}$

Add $9$ and $4$ .

$\sqrt{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{13}$

Decimal Form:

$3.60555127 \dots$

Step 5