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

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

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.

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

Step 3

Simplify.

Multiply $- 1$ by $- 3$ .

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

Add $2$ and $3$ .

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

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

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

Subtract $2$ from $- 2$ .

$\sqrt{25 + {(- 4)}^{2}}$

Raise $- 4$ to the power of $2$ .

$\sqrt{25 + 16}$

Add $25$ and $16$ .

$\sqrt{41}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{41}$

Decimal Form:

$6.40312423 \dots$

Step 5