Key to "Distance between (-1,1,3) and (4,-4,-2)?" - Plainmath

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2022-08-20

Distance between (-1,1,3) and (4,-4,-2)?

Answer & Explanation

Cora Bird

Beginner2022-08-21Added 8 answers

The distance in 3-dimensions is very similar to that in coordinate geometry (2-D).
Given two points (a,b,c) and

(a_{1}, b_{1}, c_{1})

,

d = \sqrt{{(a - a_{1})}^{2} + {(b - b_{1})}^{2} + {(c - c_{1})}^{2}}

So

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

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

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