Find the Distance Between Two Points (3,1) and (5,-2)

$(3, 1)$ and $(5, - 2)$

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.

$\sqrt{{(5 - 3)}^{2} + {((- 2) - 1)}^{2}}$

Step 3

Simplify.

Subtract $3$ from $5$ .

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

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

$\sqrt{4 + {((- 2) - 1)}^{2}}$

Subtract $1$ from $- 2$ .

$\sqrt{4 + {(- 3)}^{2}}$

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

$\sqrt{4 + 9}$

Add $4$ and $9$ .

$\sqrt{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{13}$

Decimal Form:

$3.60555127 \dots$

Step 5