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Show that the DeltaABC with vertices A (...

Show that the `DeltaABC` with vertices A ( 0,4, 1) , B ( 2, 3, -1) and C ( 4,5,0) is right angled.

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Verified by Experts

Given that vertices of the `DeltaABC` are A (0,4,1) B ( 2, 3,-1) and C ( 4,5,0)
` AB= sqrt((0-2)^(2)+(4-3)^(3)+(1+1)^(2))`
`sqrt(4+1+4)=3`
`BC=sqrt((2-4)^(2)+(3-5)^(2)+(-1-0)^(2))`
`sqrt(4+4+1)=3`
`AC=sqrt((0-4)^(2)+(4-5)^(2)+(1-0)^(2))`
`sqrt(16+1+1)=sqrt18`
`AC^(2)=AB^(2)+BC^(2)`
18=9+9
Hence, ventrices `DeltaABC` is a right angled triangle.
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