Find the Distance Between Two Points (6,-2) , (3,-9)

$(6, - 2)$ , $(3, - 9)$

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.

$\sqrt{{(3 - 6)}^{2} + {((- 9) - (- 2))}^{2}}$

Step 3

Simplify.

Subtract $6$ from $3$ .

$\sqrt{{(- 3)}^{2} + {((- 9) - (- 2))}^{2}}$

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

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

Multiply $- 1$ by $- 2$ .

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

Add $- 9$ and $2$ .

$\sqrt{9 + {(- 7)}^{2}}$

Raise $- 7$ to the power of $2$ .

$\sqrt{9 + 49}$

Add $9$ and $49$ .

$\sqrt{58}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{58}$

Decimal Form:

$7.61577310 \dots$

Step 5