Resolved: "Distance between (-6,3,4) and (-5,-1,1)?" - Plainmath

cofak48

Answered question

2022-08-13

Distance between (-6,3,4) and (-5,-1,1)?

Answer & Explanation

Luna Wells

Beginner2022-08-14Added 19 answers

You may be familiar with the two-dimensional distance formula, which tells us that the distance between

(x_{1}, y_{1})

and

(x_{2}, y_{2})

is:

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

There is a similar formula for three dimensions for the distance between

(x_{1}, y_{1}, z_{1})

and

(x_{2}, y_{2}, z_{2})

, namely:

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

So in our example, the distance between

(x_{1}, y_{1}, z_{1}) = (- 6, 3, 4)

and

(x_{2}, y_{2}, z_{2}) = (- 5, - 1, 1)

is:

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

= \sqrt{{((- 5) - (- 6))}^{2} + {((- 1) - 3)}^{2} + {(1 - 4)}^{2}}

= \sqrt{26}

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