Find the Distance Between Two Points (3,-8) and (-6,4)

$(3, - 8)$ and $(- 6, 4)$

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.

$\sqrt{{((- 6) - 3)}^{2} + {(4 - (- 8))}^{2}}$

Step 3

Simplify.

Subtract $3$ from $- 6$ .

$\sqrt{{(- 9)}^{2} + {(4 - (- 8))}^{2}}$

Raise $- 9$ to the power of $2$ .

$\sqrt{81 + {(4 - (- 8))}^{2}}$

Multiply $- 1$ by $- 8$ .

$\sqrt{81 + {(4 + 8)}^{2}}$

Add $4$ and $8$ .

$\sqrt{81 + 12^{2}}$

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

$\sqrt{81 + 144}$

Add $81$ and $144$ .

$\sqrt{225}$

Rewrite $225$ as $15^{2}$ .

$\sqrt{15^{2}}$

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

$15$

Step 4