Find the Distance Between Two Points (0,-2) and (3,1)

$(0, - 2)$ and $(3, 1)$

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.

$\sqrt{{(3 - 0)}^{2} + {(1 - (- 2))}^{2}}$

Step 3

Simplify.

Subtract $0$ from $3$ .

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

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

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

Multiply $- 1$ by $- 2$ .

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

Add $1$ and $2$ .

$\sqrt{9 + 3^{2}}$

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.

$3 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{2}$

Decimal Form:

$4.24264068 \dots$

Step 5