Find the Distance Between Two Points (4,2) and (1,-2)

$(4, 2)$ and $(1, - 2)$

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.

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

Simplify.

Subtract $4$ from $1$ .

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

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

$\sqrt{9 + {((- 2) - 2)}^{2}}$

Subtract $2$ from $- 2$ .

$\sqrt{9 + {(- 4)}^{2}}$

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

$\sqrt{9 + 16}$

Add $9$ and $16$ .

$\sqrt{25}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$5$