Calculate the distance between the points $(- 3, 6, 7)$ and $(2, - 1, 4)$ in $3 D$ space.

4.36

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5.92

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7.91

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9.11

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22.25

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Solution

The correct option is C $9.11$

We know the distance formula:

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

The coordinates are $(- 3, 6, 7)$ and $(2, - 1, 4)$

$d = \sqrt{(2 - (- 3))^{2} + ((- 1) - 6)^{2} + (4 - 7)^{2}}$

$d = \sqrt{(5)^{2} + ((- 7)^{2} + (- 3)^{2}}$

$d = \sqrt{25 + 49 + 9}$

$d = \sqrt{83}$

$d = 9.11$

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