Find the Distance Between Two Points (0,0) , (4,5)

$(0, 0)$ , $(4, 5)$

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.

$\sqrt{{(4 - 0)}^{2} + {(5 - 0)}^{2}}$

Step 3

Simplify.

Subtract $0$ from $4$ .

$\sqrt{4^{2} + {(5 - 0)}^{2}}$

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

$\sqrt{16 + {(5 - 0)}^{2}}$

Subtract $0$ from $5$ .

$\sqrt{16 + 5^{2}}$

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

$\sqrt{16 + 25}$

Add $16$ and $25$ .

$\sqrt{41}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{41}$

Decimal Form:

$6.40312423 \dots$

Step 5