Find the Distance Between Two Points (-6,8) , (2,-7)

$(- 6, 8)$ , $(2, - 7)$

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.

$\sqrt{{(2 - (- 6))}^{2} + {((- 7) - 8)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 6$ .

$\sqrt{{(2 + 6)}^{2} + {((- 7) - 8)}^{2}}$

Add $2$ and $6$ .

$\sqrt{8^{2} + {((- 7) - 8)}^{2}}$

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

$\sqrt{64 + {((- 7) - 8)}^{2}}$

Subtract $8$ from $- 7$ .

$\sqrt{64 + {(- 15)}^{2}}$

Raise $- 15$ to the power of $2$ .

$\sqrt{64 + 225}$

Add $64$ and $225$ .

$\sqrt{289}$

Rewrite $289$ as $17^{2}$ .

$\sqrt{17^{2}}$

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

$17$

Step 4