Let the plane $\pi \equiv z = x$ and the points $\mathrm { A } ( 0 , - 1,0 )$ and $\mathrm { B } ( 0,1,0 )$ belonging to the plane $\pi$. a) ( 1.25 points) If points A and B are adjacent vertices of a square with vertices $\{ \mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } \}$ that lies in the plane $\pi$, find the possible points C and D. b) ( 1.25 points) If points A and B are opposite vertices of a square that lies in the plane $\pi$, determine the other two vertices of it.
Let the plane $\pi \equiv z = x$ and the points $\mathrm { A } ( 0 , - 1,0 )$ and $\mathrm { B } ( 0,1,0 )$ belonging to the plane $\pi$.\\
a) ( 1.25 points) If points A and B are adjacent vertices of a square with vertices $\{ \mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } \}$ that lies in the plane $\pi$, find the possible points C and D.\\
b) ( 1.25 points) If points A and B are opposite vertices of a square that lies in the plane $\pi$, determine the other two vertices of it.