Find the Distance Between Two Points (6,5) , (-2,5)

$(6, 5)$ , $(- 2, 5)$

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.

$\sqrt{{((- 2) - 6)}^{2} + {(5 - 5)}^{2}}$

Step 3

Simplify.

Subtract $6$ from $- 2$ .

$\sqrt{{(- 8)}^{2} + {(5 - 5)}^{2}}$

Raise $- 8$ to the power of $2$ .

$\sqrt{64 + {(5 - 5)}^{2}}$

Subtract $5$ from $5$ .

$\sqrt{64 + 0^{2}}$

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

$\sqrt{64 + 0}$

Add $64$ and $0$ .

$\sqrt{64}$

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2}}$

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

$8$

Step 4