Find the Distance Between Two Points (p,q) , (0,0)

$(p, q)$ , $(0, 0)$

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.

$\sqrt{{(0 - p)}^{2} + {(0 - q)}^{2}}$

Step 3

Simplify.

Subtract $p$ from $0$ .

$\sqrt{{(- p)}^{2} + {(0 - q)}^{2}}$

Apply the product rule to $- p$ .

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

Raise $- 1$ to the power of $2$ .

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

Multiply $p^{2}$ by $1$ .

$\sqrt{p^{2} + {(0 - q)}^{2}}$

Subtract $q$ from $0$ .

$\sqrt{p^{2} + {(- q)}^{2}}$

Apply the product rule to $- q$ .

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

Raise $- 1$ to the power of $2$ .

$\sqrt{p^{2} + 1 q^{2}}$

Multiply $q^{2}$ by $1$ .

$\sqrt{p^{2} + q^{2}}$