Find the Distance Between Two Points (-2,1) and (4,3)

$(- 2, 1)$ and $(4, 3)$

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.

$\sqrt{{(4 - (- 2))}^{2} + {(3 - 1)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 2$ .

$\sqrt{{(4 + 2)}^{2} + {(3 - 1)}^{2}}$

Add $4$ and $2$ .

$\sqrt{6^{2} + {(3 - 1)}^{2}}$

Raise $6$ to the power of $2$ .

$\sqrt{36 + {(3 - 1)}^{2}}$

Subtract $1$ from $3$ .

$\sqrt{36 + 2^{2}}$

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

$\sqrt{36 + 4}$

Add $36$ and $4$ .

$\sqrt{40}$

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$\sqrt{4 (10)}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 10}$

Pull terms out from under the radical.

$2 \sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{10}$

Decimal Form:

$6.32455532 \dots$

Step 5