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Find the Distance Between Two Points (-2,-5) , (0,8)

$(- 2, - 5)$ ,

$(0, 8)$

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.

$\sqrt{{(0 - (- 2))}^{2} + {(8 - (- 5))}^{2}}$

Step 3

Simplify.

Multiply

$- 1$ by

$- 2$ .

$\sqrt{{(0 + 2)}^{2} + {(8 - (- 5))}^{2}}$

Add

$0$ and

$2$ .

$\sqrt{2^{2} + {(8 - (- 5))}^{2}}$

Raise

$2$ to the power of

$2$ .

$\sqrt{4 + {(8 - (- 5))}^{2}}$

Multiply

$- 1$ by

$- 5$ .

$\sqrt{4 + {(8 + 5)}^{2}}$

Add

$8$ and

$5$ .

$\sqrt{4 + 13^{2}}$

Raise

$13$ to the power of

$2$ .

$\sqrt{4 + 169}$

Add

$4$ and

$169$ .

$\sqrt{173}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{173}$

Decimal Form:

$13.15294643 \dots$

Step 5