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

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

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.

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

Step 3

Simplify.

Subtract $2$ from $3$ .

$\sqrt{1^{2} + {((- 3) - (- 2))}^{2}}$

One to any power is one.

$\sqrt{1 + {((- 3) - (- 2))}^{2}}$

Multiply $- 1$ by $- 2$ .

$\sqrt{1 + {(- 3 + 2)}^{2}}$

Add $- 3$ and $2$ .

$\sqrt{1 + {(- 1)}^{2}}$

Raise $- 1$ to the power of $2$ .

$\sqrt{1 + 1}$

Add $1$ and $1$ .

$\sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$

Step 5