Algebra Examples

$(7, 2, 9)$ ,

$(10, 1, 1)$

Step 1

To find the distance between two 3d points, square the difference of the x, y, and z points. Then, sum them and take the square root.

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

Step 2

Replace

$x_{1}$ ,

$x_{2}$ ,

$y_{1}$ ,

$y_{2}$ ,

$z_{1}$ , and

$z_{2}$ with the corresponding values.

$D i s t a n c e = \sqrt{{(10 - 7)}^{2} + {(1 - 2)}^{2} + {(1 - 9)}^{2}}$

Step 3

Simplify the expression

$\sqrt{{(10 - 7)}^{2} + {(1 - 2)}^{2} + {(1 - 9)}^{2}}$ .

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Step 3.1

Subtract

$7$ from

$10$ .

$D i s t a n c e = \sqrt{3^{2} + {(1 - 2)}^{2} + {(1 - 9)}^{2}}$

Step 3.2

Raise

$3$ to the power of

$2$ .

$D i s t a n c e = \sqrt{9 + {(1 - 2)}^{2} + {(1 - 9)}^{2}}$

Step 3.3

Subtract

$2$ from

$1$ .

$D i s t a n c e = \sqrt{9 + {(- 1)}^{2} + {(1 - 9)}^{2}}$

Step 3.4

Raise

$- 1$ to the power of

$2$ .

$D i s t a n c e = \sqrt{9 + 1 + {(1 - 9)}^{2}}$

Step 3.5

Subtract

$9$ from

$1$ .

$D i s t a n c e = \sqrt{9 + 1 + {(- 8)}^{2}}$

Step 3.6

Raise

$- 8$ to the power of

$2$ .

$D i s t a n c e = \sqrt{9 + 1 + 64}$

Step 3.7

Add

$9$ and

$1$ .

$D i s t a n c e = \sqrt{10 + 64}$

Step 3.8

Add

$10$ and

$64$ .

$D i s t a n c e = \sqrt{74}$

Step 4

The distance between

$(7, 2, 9)$ and

$(10, 1, 1)$ is

$\sqrt{74}$ .

$\sqrt{74} \approx 8.60232526$

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