Find the Distance Between Two Points (0,14) , (5,-2)

$(0, 14)$ , $(5, - 2)$

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.

$\sqrt{{(5 - 0)}^{2} + {((- 2) - 14)}^{2}}$

Step 3

Simplify.

Subtract $0$ from $5$ .

$\sqrt{5^{2} + {((- 2) - 14)}^{2}}$

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

$\sqrt{25 + {((- 2) - 14)}^{2}}$

Subtract $14$ from $- 2$ .

$\sqrt{25 + {(- 16)}^{2}}$

Raise $- 16$ to the power of $2$ .

$\sqrt{25 + 256}$

Add $25$ and $256$ .

$\sqrt{281}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{281}$

Decimal Form:

$16.76305461 \dots$

Step 5