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

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

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.

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

Step 3

Simplify.

Subtract $2$ from $- 3$ .

$\sqrt{{(- 5)}^{2} + {((- 6) - 3)}^{2}}$

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

$\sqrt{25 + {((- 6) - 3)}^{2}}$

Subtract $3$ from $- 6$ .

$\sqrt{25 + {(- 9)}^{2}}$

Raise $- 9$ to the power of $2$ .

$\sqrt{25 + 81}$

Add $25$ and $81$ .

$\sqrt{106}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{106}$

Decimal Form:

$10.29563014 \dots$

Step 5