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

$(2, 4)$ , $(2, - 2)$

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.

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

Step 3

Simplify.

Subtract $2$ from $2$ .

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

Raising $0$ to any positive power yields $0$ .

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

Subtract $4$ from $- 2$ .

$\sqrt{0 + {(- 6)}^{2}}$

Raise $- 6$ to the power of $2$ .

$\sqrt{0 + 36}$

Add $0$ and $36$ .

$\sqrt{36}$

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2}}$

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

$6$

Step 4