Find the Distance Between Two Points (-5,4) , (3,-2)

$(- 5, 4)$ , $(3, - 2)$

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.

$\sqrt{{(3 - (- 5))}^{2} + {((- 2) - 4)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 5$ .

$\sqrt{{(3 + 5)}^{2} + {((- 2) - 4)}^{2}}$

Add $3$ and $5$ .

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

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

$\sqrt{64 + {((- 2) - 4)}^{2}}$

Subtract $4$ from $- 2$ .

$\sqrt{64 + {(- 6)}^{2}}$

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

$\sqrt{64 + 36}$

Add $64$ and $36$ .

$\sqrt{100}$

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2}}$

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

$10$

Step 4