Trigonometry Examples

(- 1, - 2)

$(- 1, - 2)$ ,

(11, 7)

$(11, 7)$

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}}

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Step 2

Substitute the actual values of the points into the distance formula.

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

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

Step 3

Simplify.

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Step 3.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

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

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

Step 3.2

Add

11

$11$ and

1

$1$ .

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

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

Step 3.3

Raise

12

$12$ to the power of

2

$2$ .

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

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

Step 3.4

Multiply

- 1

$- 1$ by

- 2

$- 2$ .

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

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

Step 3.5

Add

7

$7$ and

2

$2$ .

\sqrt{144 + 9^{2}}

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

Step 3.6

Raise

9

$9$ to the power of

2

$2$ .

\sqrt{144 + 81}

$\sqrt{144 + 81}$

Step 3.7

Add

144

$144$ and

81

$81$ .

\sqrt{225}

$\sqrt{225}$

Step 3.8

Rewrite

225

$225$ as

15^{2}

$15^{2}$ .

\sqrt{15^{2}}

$\sqrt{15^{2}}$

Step 3.9

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

15

$15$

15

$15$

Step 4