Solved: "Distance between (-5,3,9) and (-1,-4,1)?"

Ashlynn Hale

Answered question

2022-08-12

Distance between (-5,3,9) and (-1,-4,1)?

pelvogp

Beginner2022-08-13Added 18 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 - (- 5))}^{2} + {(- 4 - 3)}^{2} + {(1 - 9)}^{2}}

Now we simplify:

d = \sqrt{{(4)}^{2} + {(- 7)}^{2} + {(- 8)}^{2}}

d = \sqrt{16 + 49 + 64}

d = \sqrt{129}

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

\sqrt{129}

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

d \approx 11.358

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