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25 January, 21:20

Prove the the triangle with vertices a (-2,4,0), b (1,2,-1) and c (-1,1,2) is regular.

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  1. 25 January, 21:27
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    See the offered decision:

    one way is to calculate (and compare) lengths of AB, AC and BC:

    AB² = (-2-1) ² + (4-2) ² + (0+1) ²=14;

    AC² = (-2+1) ² + (4-1) ² + (0-2) ²=14;

    BC² = (-1-1) ² + (1-2) ² + (2+1) ²=14.

    AB=AC=BC ⇒ the triangle is regular.
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