Find the Distance Between Two Points (0,-8) and (3,2)

$(0, - 8)$ and $(3, 2)$

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.

$\sqrt{{(3 - 0)}^{2} + {(2 - (- 8))}^{2}}$

Step 3

Simplify.

Subtract $0$ from $3$ .

$\sqrt{3^{2} + {(2 - (- 8))}^{2}}$

Raise $3$ to the power of $2$ .

$\sqrt{9 + {(2 - (- 8))}^{2}}$

Multiply $- 1$ by $- 8$ .

$\sqrt{9 + {(2 + 8)}^{2}}$

Add $2$ and $8$ .

$\sqrt{9 + 10^{2}}$

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

$\sqrt{9 + 100}$

Add $9$ and $100$ .

$\sqrt{109}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{109}$

Decimal Form:

$10.44030650 \dots$

Step 5