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

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

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.

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

Step 3

Simplify.

Subtract $5$ from $- 3$ .

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

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

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

Multiply $- 1$ by $- 2$ .

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

Add $4$ and $2$ .

$\sqrt{64 + 6^{2}}$

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