Find the Distance Between Two Points (-5,-3) , (1,5)

$(- 5, - 3)$ , $(1, 5)$

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.

$\sqrt{{(1 - (- 5))}^{2} + {(5 - (- 3))}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 5$ .

$\sqrt{{(1 + 5)}^{2} + {(5 - (- 3))}^{2}}$

Add $1$ and $5$ .

$\sqrt{6^{2} + {(5 - (- 3))}^{2}}$

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

$\sqrt{36 + {(5 - (- 3))}^{2}}$

Multiply $- 1$ by $- 3$ .

$\sqrt{36 + {(5 + 3)}^{2}}$

Add $5$ and $3$ .

$\sqrt{36 + 8^{2}}$

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

$\sqrt{36 + 64}$

Add $36$ and $64$ .

$\sqrt{100}$

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

$\sqrt{10^{2}}$

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

$10$

Step 4