Trigonometry Examples

$(- 1, - 2)$ , $(11, 7)$

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.

$\sqrt{{(11 - (- 1))}^{2} + {(7 - (- 2))}^{2}}$

Step 3

Simplify.

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Step 3.1

Multiply $- 1$ by $- 1$ .

$\sqrt{{(11 + 1)}^{2} + {(7 - (- 2))}^{2}}$

Step 3.2

Add $11$ and $1$ .

$\sqrt{12^{2} + {(7 - (- 2))}^{2}}$

Step 3.3

Raise $12$ to the power of $2$ .

$\sqrt{144 + {(7 - (- 2))}^{2}}$

Step 3.4

Multiply $- 1$ by $- 2$ .

$\sqrt{144 + {(7 + 2)}^{2}}$

Step 3.5

Add $7$ and $2$ .

$\sqrt{144 + 9^{2}}$

Step 3.6

Raise $9$ to the power of $2$ .

$\sqrt{144 + 81}$

Step 3.7

Add $144$ and $81$ .

$\sqrt{225}$

Step 3.8

Rewrite $225$ as $15^{2}$ .

$\sqrt{15^{2}}$

Step 3.9

Pull terms out from under the radical, assuming positive real numbers.

$15$

Step 4