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

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

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.

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

Step 3

Simplify.

Multiply $- 1$ by $- 2$ .

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

Add $3$ and $2$ .

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

Raise $5$ to the power of $2$ .

$\sqrt{25 + {(5 - (- 5))}^{2}}$

Multiply $- 1$ by $- 5$ .

$\sqrt{25 + {(5 + 5)}^{2}}$

Add $5$ and $5$ .

$\sqrt{25 + 10^{2}}$

Raise $10$ to the power of $2$ .

$\sqrt{25 + 100}$

Add $25$ and $100$ .

$\sqrt{125}$

Rewrite $125$ as $5^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$\sqrt{25 (5)}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 5}$

Pull terms out from under the radical.

$5 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{5}$

Decimal Form:

$11.18033988 \dots$

Step 5