Trigonometry Examples

$(- 3, 8)$ , $(- 1, 6)$

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.

$\sqrt{{((- 1) - (- 3))}^{2} + {(6 - 8)}^{2}}$

Step 3

Simplify.

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Step 3.1

Multiply $- 1$ by $- 3$ .

$\sqrt{{(- 1 + 3)}^{2} + {(6 - 8)}^{2}}$

Step 3.2

Add $- 1$ and $3$ .

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

Step 3.3

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

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

Step 3.4

Subtract $8$ from $6$ .

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

Step 3.5

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

$\sqrt{4 + 4}$

Step 3.6

Add $4$ and $4$ .

$\sqrt{8}$

Step 3.7

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 3.7.1

Factor $4$ out of $8$ .

$\sqrt{4 (2)}$

Step 3.7.2

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

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

Step 3.8

Pull terms out from under the radical.

$2 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2}$

Decimal Form:

$2.82842712 \dots$

Step 5