Find the Distance Between Two Points (-3,1) and (7,-3)

$(- 3, 1)$ and $(7, - 3)$

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.

$\sqrt{{(7 - (- 3))}^{2} + {((- 3) - 1)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 3$ .

$\sqrt{{(7 + 3)}^{2} + {((- 3) - 1)}^{2}}$

Add $7$ and $3$ .

$\sqrt{10^{2} + {((- 3) - 1)}^{2}}$

Raise $10$ to the power of $2$ .

$\sqrt{100 + {((- 3) - 1)}^{2}}$

Subtract $1$ from $- 3$ .

$\sqrt{100 + {(- 4)}^{2}}$

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

$\sqrt{100 + 16}$

Add $100$ and $16$ .

$\sqrt{116}$

Rewrite $116$ as $2^{2} \cdot 29$ .

Factor $4$ out of $116$ .

$\sqrt{4 (29)}$

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

$\sqrt{2^{2} \cdot 29}$

Pull terms out from under the radical.

$2 \sqrt{29}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{29}$

Decimal Form:

$10.77032961 \dots$

Step 5