Find the Distance Between Two Points (-3,9) and (2,5)

$(- 3, 9)$ and $(2, 5)$

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.

$\sqrt{{(2 - (- 3))}^{2} + {(5 - 9)}^{2}}$

Simplify.

Multiply $- 1$ by $- 3$ .

$\sqrt{{(2 + 3)}^{2} + {(5 - 9)}^{2}}$

Add $2$ and $3$ .

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

Raise $5$ to the power of $2$ .

$\sqrt{25 + {(5 - 9)}^{2}}$

Subtract $9$ from $5$ .

$\sqrt{25 + {(- 4)}^{2}}$

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

$\sqrt{25 + 16}$

Add $25$ and $16$ .

$\sqrt{41}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{41}$

Decimal Form:

$6.40312423 \dots$