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saborcehj

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2022-08-21

What is the distance between (-1,4,1) and (6,-7,-2)?

Arjun Wright

Beginner2022-08-22Added 8 answers

The formula for the distance for 3-dimensional coordinates is similar or 2-dimensional; it is:

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

We have the two coordinates, so we can plug in the values for x, y, and z:

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

Now we simplify:

d = \sqrt{{(- 3)}^{2} + {(- 11)}^{2} + {(7)}^{2}}

d = \sqrt{179}

If you want to leave it in exact form, you can leave the distance as

\sqrt{179}

. However, if you want the decimal answer, here it is rounded to the nearest hundblackth's place:

d \approx 13.38

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