Find the Distance Between Two Points (-1,3) , (2,-2)

$(- 1, 3)$ , $(2, - 2)$

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.

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

Step 3

Simplify.

Multiply $- 1$ by $- 1$ .

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

Add $2$ and $1$ .

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

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

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

Subtract $3$ from $- 2$ .

$\sqrt{9 + {(- 5)}^{2}}$

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

$\sqrt{9 + 25}$

Add $9$ and $25$ .

$\sqrt{34}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{34}$

Decimal Form:

$5.83095189 \dots$

Step 5