Find the Distance Between Two Points (2,-8) and (5,-6)

$(2, - 8)$ and $(5, - 6)$

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.

$\sqrt{{(5 - 2)}^{2} + {((- 6) - (- 8))}^{2}}$

Step 3

Simplify.

Subtract $2$ from $5$ .

$\sqrt{3^{2} + {((- 6) - (- 8))}^{2}}$

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

$\sqrt{9 + {((- 6) - (- 8))}^{2}}$

Multiply $- 1$ by $- 8$ .

$\sqrt{9 + {(- 6 + 8)}^{2}}$

Add $- 6$ and $8$ .

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

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

$\sqrt{9 + 4}$

Add $9$ and $4$ .

$\sqrt{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{13}$

Decimal Form:

$3.60555127 \dots$

Step 5