Key to "Distance between (13,23,-1) and (-3,17,2)?" - Plainmath

on2t1inf8b

Answered question

2022-07-19

Distance between (13,23,-1) and (-3,17,2)?

Answer & Explanation

sviudes7w

Beginner2022-07-20Added 12 answers

To calculate the distance between the 2 points use the three dimensional form of the distance formula :

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

w h e r e (x_{1}, y_{1}, z_{1}), (x_{2}, y_{2}, z_{2})

are 2 points
In this question let

(x_{1}, y_{!}, z_{1}) = (13, 23, - 1)

and

(x_{2}, y_{2}, z_{2}) = (- 3, 17, 2)

substitute into the formula :

d = \sqrt{{(- 3 - 13)}^{2} + {(17 - 23)}^{2} + {(2 - (- 1))}^{2}}

= \sqrt{{(- 16)}^{2} + {(- 6)}^{2} + 3^{2}}

\Rightarrow d = \sqrt{256 + 36 + 9} = \sqrt{301}

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