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The quadrilateral formed by the points $A(1,2,5), B(-1,6,1), C(3,4,-3)$ and $D(5,0,1)$ is a
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Verified Answer
The correct answer is:
Square
Vertices of quadrilateral
$\begin{aligned}
& A(1,2,5), B(-1,6,1), C(3,4,-3), D(5,0,1) \\
& \therefore \quad A B=\sqrt{4+16+16}=6 \\
& B C=\sqrt{16+4+16}=6 \\
& C D=\sqrt{4+16+16}=6 \\
& A D=\sqrt{16+4+16}=6 \\
& A C=\sqrt{4+4+64}=\sqrt{72} \\
& B D=\sqrt{36+36+0}=\sqrt{72} \\
& \text { Here, } \quad A B=B C=C D=A D \text { and } A C=B D \\
&
\end{aligned}$
$\therefore A B C D$ forms a square.
$\begin{aligned}
& A(1,2,5), B(-1,6,1), C(3,4,-3), D(5,0,1) \\
& \therefore \quad A B=\sqrt{4+16+16}=6 \\
& B C=\sqrt{16+4+16}=6 \\
& C D=\sqrt{4+16+16}=6 \\
& A D=\sqrt{16+4+16}=6 \\
& A C=\sqrt{4+4+64}=\sqrt{72} \\
& B D=\sqrt{36+36+0}=\sqrt{72} \\
& \text { Here, } \quad A B=B C=C D=A D \text { and } A C=B D \\
&
\end{aligned}$
$\therefore A B C D$ forms a square.
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