Find the Distance Between Two Points (-3,4) , (5,-6)

$(- 3, 4)$ , $(5, - 6)$

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.

$\sqrt{{(5 - (- 3))}^{2} + {((- 6) - 4)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 3$ .

$\sqrt{{(5 + 3)}^{2} + {((- 6) - 4)}^{2}}$

Add $5$ and $3$ .

$\sqrt{8^{2} + {((- 6) - 4)}^{2}}$

Raise $8$ to the power of $2$ .

$\sqrt{64 + {((- 6) - 4)}^{2}}$

Subtract $4$ from $- 6$ .

$\sqrt{64 + {(- 10)}^{2}}$

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

$\sqrt{64 + 100}$

Add $64$ and $100$ .

$\sqrt{164}$

Rewrite $164$ as $2^{2} \cdot 41$ .

Factor $4$ out of $164$ .

$\sqrt{4 (41)}$

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

$\sqrt{2^{2} \cdot 41}$

Pull terms out from under the radical.

$2 \sqrt{41}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{41}$

Decimal Form:

$12.80624847 \dots$

Step 5