Find the Distance Between Two Points (-2,4) and (4,-6)

$(- 2, 4)$ and $(4, - 6)$

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.

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

Step 3

Simplify.

Multiply $- 1$ by $- 2$ .

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

Add $4$ and $2$ .

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

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

$\sqrt{36 + {((- 6) - 4)}^{2}}$

Subtract $4$ from $- 6$ .

$\sqrt{36 + {(- 10)}^{2}}$

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

$\sqrt{36 + 100}$

Add $36$ and $100$ .

$\sqrt{136}$

Rewrite $136$ as $2^{2} \cdot 34$ .

Factor $4$ out of $136$ .

$\sqrt{4 (34)}$

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

$\sqrt{2^{2} \cdot 34}$

Pull terms out from under the radical.

$2 \sqrt{34}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{34}$

Decimal Form:

$11.66190378 \dots$

Step 5