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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