Find the Distance Between Two Points (0,-2) and (5,3)

$(0, - 2)$ and $(5, 3)$

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.

$\sqrt{{(5 - 0)}^{2} + {(3 - (- 2))}^{2}}$

Step 3

Simplify.

Subtract $0$ from $5$ .

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

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

$\sqrt{25 + {(3 - (- 2))}^{2}}$

Multiply $- 1$ by $- 2$ .

$\sqrt{25 + {(3 + 2)}^{2}}$

Add $3$ and $2$ .

$\sqrt{25 + 5^{2}}$

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

$\sqrt{25 + 25}$

Add $25$ and $25$ .

$\sqrt{50}$

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2)}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 2}$

Pull terms out from under the radical.

$5 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{2}$

Decimal Form:

$7.07106781 \dots$

Step 5