Precalculus Examples

(- 5, - 7)

$(- 5, - 7)$ ,

(5, - 2)

$(5, - 2)$

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{{(5 - (- 5))}^{2} + {((- 2) - (- 7))}^{2}}

$\sqrt{{(5 - (- 5))}^{2} + {((- 2) - (- 7))}^{2}}$

Step 3

Simplify.

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Step 3.1

Multiply

- 1

$- 1$ by

- 5

$- 5$ .

\sqrt{{(5 + 5)}^{2} + {((- 2) - (- 7))}^{2}}

$\sqrt{{(5 + 5)}^{2} + {((- 2) - (- 7))}^{2}}$

Step 3.2

Add

5

$5$ and

5

$5$ .

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

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

Step 3.3

Raise

10

$10$ to the power of

2

$2$ .

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

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

Step 3.4

Multiply

- 1

$- 1$ by

- 7

$- 7$ .

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

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

Step 3.5

Add

- 2

$- 2$ and

7

$7$ .

\sqrt{100 + 5^{2}}

$\sqrt{100 + 5^{2}}$

Step 3.6

Raise

5

$5$ to the power of

2

$2$ .

\sqrt{100 + 25}

$\sqrt{100 + 25}$

Step 3.7

Add

100

$100$ and

25

$25$ .

\sqrt{125}

$\sqrt{125}$

Step 3.8

Rewrite

125

$125$ as

5^{2} \cdot 5

$5^{2} \cdot 5$ .

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Step 3.8.1

Factor

25

$25$ out of

125

$125$ .

\sqrt{25 (5)}

$\sqrt{25 (5)}$

Step 3.8.2

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

\sqrt{5^{2} \cdot 5}

$\sqrt{5^{2} \cdot 5}$

\sqrt{5^{2} \cdot 5}

$\sqrt{5^{2} \cdot 5}$

Step 3.9

Pull terms out from under the radical.

5 \sqrt{5}

$5 \sqrt{5}$

5 \sqrt{5}

$5 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

5 \sqrt{5}

$5 \sqrt{5}$

Decimal Form:

11.18033988 \dots

$11.18033988 \dots$

Step 5

(- 5, - 7) (5, - 2)

$(- 5, - 7) (5, - 2)$

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