Pre-Algebra Examples

(- 3, 9)

$(- 3, 9)$ ,

(0, 9)

$(0, 9)$

Step 1

Use the distance formula to determine the distance between the two points.

Distance = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{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{{(0 - (- 3))}^{2} + {(9 - 9)}^{2}}

$\sqrt{{(0 - (- 3))}^{2} + {(9 - 9)}^{2}}$

Step 3

Simplify.

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Step 3.1

Multiply

- 1

$- 1$ by

- 3

$- 3$ .

\sqrt{{(0 + 3)}^{2} + {(9 - 9)}^{2}}

$\sqrt{{(0 + 3)}^{2} + {(9 - 9)}^{2}}$

Step 3.2

Add

0

$0$ and

3

$3$ .

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

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

Step 3.3

Raise

3

$3$ to the power of

2

$2$ .

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

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

Step 3.4

Subtract

9

$9$ from

9

$9$ .

\sqrt{9 + 0^{2}}

$\sqrt{9 + 0^{2}}$

Step 3.5

Raising

0

$0$ to any positive power yields

0

$0$ .

\sqrt{9 + 0}

$\sqrt{9 + 0}$

Step 3.6

Add

9

$9$ and

0

$0$ .

\sqrt{9}

$\sqrt{9}$

Step 3.7

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

\sqrt{3^{2}}

$\sqrt{3^{2}}$

Step 3.8

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

3

$3$

3

$3$

Step 4

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