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

$(0, 0)$ , $(1, 4)$

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.

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

Step 3

Simplify.

Subtract $0$ from $1$ .

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

One to any power is one.

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

Subtract $0$ from $4$ .

$\sqrt{1 + 4^{2}}$

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

$\sqrt{1 + 16}$

Add $1$ and $16$ .

$\sqrt{17}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{17}$

Decimal Form:

$4.12310562 \dots$

Step 5