Ejemplos

(7, 2, 9)

$(7, 2, 9)$ ,

(10, 1, 1)

$(10, 1, 1)$

Paso 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}^{2} + {(y_{2} - y_{1})}_{2}^{2} + {(z_{2} - z_{1})}_{2}^{2}}

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

Paso 2

Reemplaza

x_{1}

$x_{1}$ ,

x_{2}

$x_{2}$ ,

y_{1}

$y_{1}$ ,

y_{2}

$y_{2}$ ,

z_{1}

$z_{1}$ y

z_{2}

$z_{2}$ con los valores correspondientes.

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

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

Paso 3

Simplifica la expresión

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

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

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Paso 3.1

Resta

7

$7$ de

10

$10$ .

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

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

Paso 3.2

Eleva

3

$3$ a la potencia de

2

$2$ .

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

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

Paso 3.3

Resta

2

$2$ de

1

$1$ .

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

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

Paso 3.4

Eleva

- 1

$- 1$ a la potencia de

2

$2$ .

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

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

Paso 3.5

Resta

9

$9$ de

1

$1$ .

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

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

Paso 3.6

Eleva

- 8

$- 8$ a la potencia de

2

$2$ .

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

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

Paso 3.7

Suma

9

$9$ y

1

$1$ .

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

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

Paso 3.8

Suma

10

$10$ y

64

$64$ .

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

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

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

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

Paso 4

La distancia entre

(7, 2, 9)

$(7, 2, 9)$ y

(10, 1, 1)

$(10, 1, 1)$ es

\sqrt{74}

$\sqrt{74}$ .

\sqrt{74} \approx 8.60232526

$\sqrt{74} \approx 8.60232526$

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