Solved: "Distance between (-5,13,-14) and (-11,4,1)?" - Plainmath

Ralzereep9h

Answered question

2022-10-15

Distance between (-5,13,-14) and (-11,4,1)?

Answer & Explanation

Messiah Trevino

Beginner2022-10-16Added 18 answers

Treat the way you would a triangle using Pythagoras but with 3 values instead of two.
Let the length between the two points be L
Let point 1

\to P_{1} \to (x_{1}, y_{1}, z_{1}) \to (- 5, 13, - 14)

Let point 2

\to P_{2} \to (x_{2}, y_{2}, z_{2}) \to (- 11, 4, 1)

Then

L^{2} = {(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2} + {(z_{2} - z_{1})}^{2}

So

L = \sqrt{{(- 11 - [- 5])}^{2} + {(4 - 13)}^{2} + {(1 - [- 14])}^{2}}

L = \sqrt{36 + 81 + 225} = \sqrt{342}

But

342 = 2 \times 3^{2} \times 19

but both 19 and 2 are prime numbers

\Rightarrow L = 3 \sqrt{38}

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