Find the Distance Between Two Points (-2,8) and (3,4)

$(- 2, 8)$ and $(3, 4)$

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.

$\sqrt{{(3 - (- 2))}^{2} + {(4 - 8)}^{2}}$

Simplify.

Multiply $- 1$ by $- 2$ .

$\sqrt{{(3 + 2)}^{2} + {(4 - 8)}^{2}}$

Add $3$ and $2$ .

$\sqrt{5^{2} + {(4 - 8)}^{2}}$

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

$\sqrt{25 + {(4 - 8)}^{2}}$

Subtract $8$ from $4$ .

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

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:

$6.40312423 \dots$