Find the Distance Between Two Points (20,-5) , (-4,-2)

$(20, - 5)$ , $(- 4, - 2)$

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Substitute the actual values of the points into the distance formula.

$\sqrt{{((- 4) - 20)}^{2} + {((- 2) - (- 5))}^{2}}$

Simplify.

Subtract $20$ from $- 4$ .

$\sqrt{{(- 24)}^{2} + {((- 2) - (- 5))}^{2}}$

Raise $- 24$ to the power of $2$ .

$\sqrt{576 + {((- 2) - (- 5))}^{2}}$

Multiply $- 1$ by $- 5$ .

$\sqrt{576 + {(- 2 + 5)}^{2}}$

Add $- 2$ and $5$ .

$\sqrt{576 + 3^{2}}$

Raise $3$ to the power of $2$ .

$\sqrt{576 + 9}$

Add $576$ and $9$ .

$\sqrt{585}$

Rewrite $585$ as $3^{2} \cdot 65$ .

Factor $9$ out of $585$ .

$\sqrt{9 (65)}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 65}$

Pull terms out from under the radical.

$3 \sqrt{65}$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{65}$

Decimal Form:

$24.18677324 \dots$