"What is the distance between (5,-2,4) and (8,8,-1)?" was answered by our experts

Jean Farrell

Answered question

2022-09-27

What is the distance between (5,-2,4) and (8,8,-1)?

belidla5a

Beginner2022-09-28Added 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{{(- 1 - 4)}^{2} + {(8 - (- 2))}^{2} + {(8 - 5)}^{2}}

Now we simplify:

d = \sqrt{{(- 5)}^{2} + {(10)}^{2} + {(3)}^{2}}

d = \sqrt{134}

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

\sqrt{134}

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

d \approx 11.58

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