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Standard XII
Mathematics
Distance Formula
Question

Shown that the point (5,−1,1),(7,−4,7),(1,−6,10) and (−1,−3,4) are the vertices of a rhombus.

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Solution
Verified by Toppr

For a quadrant to be rhombus, four side of quadrant be equal.
By distance formula:
S1=√(7−5)2+(−4+1)2+(7−1)2=7S2=√(1−7)2+(−6+4)2+(10−7)2=7S3=√(−1−1)2+(−6+4)2+(10−7)2=7S4=√(−1−5)2+(−3+1)2+(4−1)2=7∵S1=S2=S3=S4
Hence the given quadrant is rhombus

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Shown that the point (5,−1,1),(7,−4,7),(1,−6,10) and (−1,−3,4) are the vertices of a rhombus.
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