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Show that the points A(2,-1,3),B(1,-3,1)...

Show that the points A(2,-1,3),B(1,-3,1) and C(0,1,2) are the vertices of an isosceles right angled triangle.

Text Solution

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The correct Answer is:
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`AB=sqrt((1-2)^(2)+(-3+1)^(2)+(1-3)^(2))`
`=sqrt(1+4+4)=3` units
`BC=sqrt((0-1)^(2)+(1+3)^(2)+(2-1)^(2))`
`=sqrt(1+16+1)=3sqrt(2)` units
and `AC=sqrt((0-2)^(2)+(1+1)^(2)+(2-3)^(2))`
`=sqrt(4+4+1)=3` units
`because AB=AC`
`therefore Delta ABC` is isosceles.
`because AB^(2)+AC^(2)=3^(2)+3^(2)=18`
`=(3sqrt(2))^(2)=BC^(2)`
`therefore Delta ABC` is right angled.
Therefore, `Delta ABC` is an isosceles right angled triangle.
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