Find the Distance Between Two Points (-4,15) , (22,3)

$(- 4, 15)$ , $(22, 3)$

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.

$\sqrt{{(22 - (- 4))}^{2} + {(3 - 15)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 4$ .

$\sqrt{{(22 + 4)}^{2} + {(3 - 15)}^{2}}$

Add $22$ and $4$ .

$\sqrt{26^{2} + {(3 - 15)}^{2}}$

Raise $26$ to the power of $2$ .

$\sqrt{676 + {(3 - 15)}^{2}}$

Subtract $15$ from $3$ .

$\sqrt{676 + {(- 12)}^{2}}$

Raise $- 12$ to the power of $2$ .

$\sqrt{676 + 144}$

Add $676$ and $144$ .

$\sqrt{820}$

Rewrite $820$ as $2^{2} \cdot 205$ .

Factor $4$ out of $820$ .

$\sqrt{4 (205)}$

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

$\sqrt{2^{2} \cdot 205}$

Pull terms out from under the radical.

$2 \sqrt{205}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{205}$

Decimal Form:

$28.63564212 \dots$

Step 5