Examples

(5, 4, 3)

$(5, 4, 3)$ ,

(2, 7, 4)

$(2, 7, 4)$

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}}

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

Step 2

Replace

x_{1}

$x_{1}$ ,

x_{2}

$x_{2}$ ,

y_{1}

$y_{1}$ ,

y_{2}

$y_{2}$ ,

z_{1}

$z_{1}$ , and

z_{2}

$z_{2}$ with the corresponding values.

D i s t a n c e = \sqrt{{(2 - 5)}^{2} + {(7 - 4)}^{2} + {(4 - 3)}^{2}}

$D i s t a n c e = \sqrt{{(2 - 5)}^{2} + {(7 - 4)}^{2} + {(4 - 3)}^{2}}$

Step 3

Simplify the expression

\sqrt{{(2 - 5)}^{2} + {(7 - 4)}^{2} + {(4 - 3)}^{2}}

$\sqrt{{(2 - 5)}^{2} + {(7 - 4)}^{2} + {(4 - 3)}^{2}}$ .

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Step 3.1

Subtract

5

$5$ from

2

$2$ .

D i s t a n c e = \sqrt{{(- 3)}^{2} + {(7 - 4)}^{2} + {(4 - 3)}^{2}}

$D i s t a n c e = \sqrt{{(- 3)}^{2} + {(7 - 4)}^{2} + {(4 - 3)}^{2}}$

Step 3.2

Raise

- 3

$- 3$ to the power of

2

$2$ .

D i s t a n c e = \sqrt{9 + {(7 - 4)}^{2} + {(4 - 3)}^{2}}

$D i s t a n c e = \sqrt{9 + {(7 - 4)}^{2} + {(4 - 3)}^{2}}$

Step 3.3

Subtract

4

$4$ from

7

$7$ .

D i s t a n c e = \sqrt{9 + 3^{2} + {(4 - 3)}^{2}}

$D i s t a n c e = \sqrt{9 + 3^{2} + {(4 - 3)}^{2}}$

Step 3.4

Raise

3

$3$ to the power of

2

$2$ .

D i s t a n c e = \sqrt{9 + 9 + {(4 - 3)}^{2}}

$D i s t a n c e = \sqrt{9 + 9 + {(4 - 3)}^{2}}$

Step 3.5

Subtract

3

$3$ from

4

$4$ .

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

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

Step 3.6

One to any power is one.

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

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

Step 3.7

Add

9

$9$ and

9

$9$ .

D i s t a n c e = \sqrt{18 + 1}

$D i s t a n c e = \sqrt{18 + 1}$

Step 3.8

Add

18

$18$ and

1

$1$ .

D i s t a n c e = \sqrt{19}

$D i s t a n c e = \sqrt{19}$

D i s t a n c e = \sqrt{19}

$D i s t a n c e = \sqrt{19}$

Step 4

The distance between

(5, 4, 3)

$(5, 4, 3)$ and

(2, 7, 4)

$(2, 7, 4)$ is

\sqrt{19}

$\sqrt{19}$ .

\sqrt{19} \approx 4.35889894

$\sqrt{19} \approx 4.35889894$

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