Find the Distance Between Two Points (1,9) and (-2,6)

$(1, 9)$ and $(- 2, 6)$

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Substitute the actual values of the points into the distance formula.

$\sqrt{{((- 2) - 1)}^{2} + {(6 - 9)}^{2}}$

Simplify.

Subtract $1$ from $- 2$ .

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

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

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

Subtract $9$ from $6$ .

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

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

$\sqrt{9 + 9}$

Add $9$ and $9$ .

$\sqrt{18}$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$\sqrt{9 (2)}$

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

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

Pull terms out from under the radical.

$3 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{2}$

Decimal Form:

$4.24264068 \dots$