Find the Distance Between Two Points (0,-3) and (4,1)

$(0, - 3)$ and $(4, 1)$

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.

$\sqrt{{(4 - 0)}^{2} + {(1 - (- 3))}^{2}}$

Step 3

Simplify.

Subtract $0$ from $4$ .

$\sqrt{4^{2} + {(1 - (- 3))}^{2}}$

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

$\sqrt{16 + {(1 - (- 3))}^{2}}$

Multiply $- 1$ by $- 3$ .

$\sqrt{16 + {(1 + 3)}^{2}}$

Add $1$ and $3$ .

$\sqrt{16 + 4^{2}}$

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

$\sqrt{16 + 16}$

Add $16$ and $16$ .

$\sqrt{32}$

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$\sqrt{16 (2)}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 2}$

Pull terms out from under the radical.

$4 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{2}$

Decimal Form:

$5.65685424 \dots$

Step 5