NSW Y8 Maths Graphing Linear Equations The Number Plane

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The Number Plane Theory

\begin{minipage}[c]{9cm} If \(x\) is positive and \(y\) is positive then the point \(P(x, y)\) lies in the first quadrant (I)\\  If \(x\) is negative and \(y\) is positive then the point \(P(-x, y)\) lies in the second quadrant (II)\\  Th \(x\) is negative and \(y\) is negative then the point \(P(-x,-y)\) lies in the third quadrant (III)\\  If \(x\) is positive and \(y\) is negative then the point \(P(x,-y)\) lies in the fourth quadrant (IV) \end{minipage}\qquad \quad  \begin{minipage}[c]{3cm} \begin{tikzpicture}[scale=0.8] \def \xmax{10} \def \xmin{-10} \def \ymax{10} \def \ymin{-10} \def \xlabel{x} \def \ylabel{y}  \begin{axis}[         axis lines=middle,     axis line style={shorten >=-10pt, shorten <=-10pt,very thick,Stealth-Stealth},         %grid=both, %major,         major grid style={line width=1pt,draw=black!70},         minor x tick num=4,         minor y tick num=4,         ylabel = $y$,         xlabel = $x$,         width=3in, height=3in,         ymin=\ymin, ymax=\ymax,         xmin=\xmin, xmax=\xmax,         axis on top=false,         axis line style = thick,         major tick style = thick,         xtick distance = 1, xlabel style={at={(ticklabel* cs:1.05)},anchor=west},         x grid style={thin, opacity=1},         ytick distance = 1, ylabel style={at={(ticklabel* cs:1.05)},anchor=south},         y grid style={thin, opacity=1},         axis on top=false,         minor xtick={-11,-10,...,10,11},         minor ytick={-11,-10,...,10,11},         xtick={-11,-10,-5,5,10,11},         ytick={-11,-10,-5,5,10,11},          nodes near coords style={         anchor=center,         inner sep=0,         color=black,         font=,},     ] \addplot[     color=red,     mark=*,      mark size=0,      only marks,     nodes near coords,     point meta=explicit symbolic,     visualization depends on={value \thisrow{label} \as \label},     ]     table[meta=label] {         x     y    label         -6    7    {2nd Quadrant}         6     7    {1st Quadrant}         -6   -7    {3rd Quadrant}         6    -7    {4th Quadrant}     }; \end{axis} \end{tikzpicture} \end{minipage}  \begin{multicols}{2}  \textbf{Example 1}\\ In which quadrants do the points lie\\ \textbf{i)} \(P(-1,3)\)\\ \textbf{ii)} \(Q(2,5)\)\\  \textbf{Example 1 solution}\\ \textbf{i)} \(x<0\) and \(y>0 \quad \therefore\) II\\ \textbf{ii)} \(x>0\) and \(y>0 \quad \therefore I\)  \columnbreak \textbf{Example 2}\\ In which quadrants do the points lie\\ \textbf{i)} \(L(-1,-2)\)\\ \textbf{ii)} \(M(6,-3)\)\\  \textbf{Example 2 solution}\\ \textbf{i)} \(x<0\) and \(y<0 \quad \therefore\) III\\ \textbf{ii)} \(x>0\) and \(y<0 \quad \therefore\) IV \end{multicols}

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Videos

Videos relating to The Number Plane.

  • The Number Plane - Video - Identify the Quadrant of a Point on the Coordinate Plane

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