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%TCIDATA{<META NAME="Title" CONTENT="Reference/Mathematics/Half Planes and Quadrants">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Mon Feb 10 15:47:27 1997}
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\section{\ Half Planes and Quadrants\label{Half planes}\label{Quadrants}}

\begin{theorem}
The coordinate axes separate the plane into four regions, called \textbf{%
quadrants}, such that if $A$ and $B$ are points not on either axis and in
the same quadrant, then the segment $\overline{AB}$ does not meet either
axis, whereas if $A$ and $B$ are in different quadrants, then $\overline{AB}$
meets at least one of the axes.
\end{theorem}

\subsubsection{Half Planes}

The half plane that contains the

\begin{itemize}
\begin{itemize}
\item  positive axis of abscissas is called the \textbf{right half plane}

\item  negative axis of abscissas is called the \textbf{left half plane}

\item  positive axis of ordinates is called the \textbf{upper half plane}

\item  negative axis of ordinates is called the \textbf{lower half plane}
\end{itemize}
\end{itemize}

\subsubsection{Quadrants}

The quadrant that is in the

\begin{itemize}
\begin{itemize}
\item  \textit{upper} half plane and \textit{right} half plane is the 
\textbf{first quadrant}

\item  \textit{upper} half plane and \textit{left} half plane is the \textbf{%
second quadrant}

\item  \textit{lower} half plane and \textit{left} half plane is the \textbf{%
third quadrant}

\item  \textit{lower} half plane and \textit{right} half plane is the 
\textbf{fourth quadrant}\hfill 
\end{itemize}
\end{itemize}

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