Precalculus Examples

(- 7, 7)

$(- 7, 7)$ ,

(3, 9)

$(3, 9)$

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{{(3 - (- 7))}^{2} + {(9 - 7)}^{2}}

$\sqrt{{(3 - (- 7))}^{2} + {(9 - 7)}^{2}}$

Step 3

Simplify.

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Step 3.1

Multiply

- 1

$- 1$ by

- 7

$- 7$ .

\sqrt{{(3 + 7)}^{2} + {(9 - 7)}^{2}}

$\sqrt{{(3 + 7)}^{2} + {(9 - 7)}^{2}}$

Step 3.2

Add

3

$3$ and

7

$7$ .

\sqrt{10^{2} + {(9 - 7)}^{2}}

$\sqrt{10^{2} + {(9 - 7)}^{2}}$

Step 3.3

Raise

10

$10$ to the power of

2

$2$ .

\sqrt{100 + {(9 - 7)}^{2}}

$\sqrt{100 + {(9 - 7)}^{2}}$

Step 3.4

Subtract

7

$7$ from

9

$9$ .

\sqrt{100 + 2^{2}}

$\sqrt{100 + 2^{2}}$

Step 3.5

Raise

2

$2$ to the power of

2

$2$ .

\sqrt{100 + 4}

$\sqrt{100 + 4}$

Step 3.6

Add

100

$100$ and

4

$4$ .

\sqrt{104}

$\sqrt{104}$

Step 3.7

Rewrite

104

$104$ as

2^{2} \cdot 26

$2^{2} \cdot 26$ .

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Step 3.7.1

Factor

4

$4$ out of

104

$104$ .

\sqrt{4 (26)}

$\sqrt{4 (26)}$

Step 3.7.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

\sqrt{2^{2} \cdot 26}

$\sqrt{2^{2} \cdot 26}$

\sqrt{2^{2} \cdot 26}

$\sqrt{2^{2} \cdot 26}$

Step 3.8

Pull terms out from under the radical.

2 \sqrt{26}

$2 \sqrt{26}$

2 \sqrt{26}

$2 \sqrt{26}$

Step 4

The result can be shown in multiple forms.

Exact Form:

2 \sqrt{26}

$2 \sqrt{26}$

Decimal Form:

10.19803902 \dots

$10.19803902 \dots$

Step 5

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