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%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Fri Oct 31 18:06:17 1997}
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\input{tcilatex}
\begin{document}


\subsection{Text}

\section{MEC}

\section{Equation of Straight Lines}

\subsubsection{\protect\small by Suen CY, moderated by Yang WC}

Your Name: 
%TCIMACRO{\HTML{<Input TYPE="Text" NAME="STUDENTNAME" VALUE=" " SIZE=0>}}
%BeginExpansion
%%
%EndExpansion

\vspace{1pt}

\subsection{Setup}

Choice Space:\ 2

Choices: Break, Radio Buttons, Permute

Question Space:1

Title:equation of straight line

\section{Question}

\subsection{Setup}

$k:=\func{rand}(3,10)$

$m:=2\times \func{rand}(1,5)+1$

$K:=11$

$H:=12$

Conditions: $\gcd (m,k)=1$

Conditions: $\gcd (m,K)=1$

Conditions: $\gcd (m,H)=1$

Conditions: $(\frac{2}{11}<\frac{m}{k})\wedge (\frac{m}{k}<\frac{10}{11})$

$p:=\func{rand}(1,2)$

$q:=(-1)^{p}$

$n:=kq$

$f=\frac{m}{n}x+\frac{m}{2n}$

$g=\frac{-n}{m}x+2$

\subsection{Comment}

\vspace{1pt}We choose L1 always passes (0,-0.5) and L2 passes (2,0) for the
graph

gradient of L1 conditioned so that it appears fully in the graph

\vspace{1pt}

choice 1: parallel line (m/n)

\vspace{1pt}choice 2: use (-m/n) as answer (forget to find 1/gradient)

\vspace{1pt}choice 3: use (n/m) as answer (forget -ve sign)

choice 4: (key) gradient:-n/m

\subsection{Statement}

Which of the following straight line is perpendicular to the straight line $%
L_{1}:%
%TCIMACRO{\FORMULA{2mx-2ny+m=0}{2mx-2ny+m=0}{evaluate}}
%BeginExpansion
2mx-2ny+m=0%
%EndExpansion
$:

\subsection{Choices}

\begin{itemize}
\item  $L_{2:\text{ }}%
%TCIMACRO{\FORMULA{ny=mx+2n}{ny=mx+2n}{evaluate}}
%BeginExpansion
ny=mx+2n%
%EndExpansion
$

\item  $L_{2:}%
%TCIMACRO{\FORMULA{ny=-mx+2n}{ny=-mx+2n}{evaluate}}
%BeginExpansion
ny=-mx+2n%
%EndExpansion
$

\item  $L_{2:}%
%TCIMACRO{\FORMULA{my=nx+2m}{my=nx+2m}{evaluate}}
%BeginExpansion
my=nx+2m%
%EndExpansion
$

\item  $L_{2:\text{ }}%
%TCIMACRO{\FORMULA{my=-nx+2m}{my=-nx+2m}{evaluate}}
%BeginExpansion
my=-nx+2m%
%EndExpansion
\correctchoice{}$
\end{itemize}

\subsection{Answer}

$L_{2:\text{ }}%
%TCIMACRO{\FORMULA{my=-nx+2m}{my=-nx+2m}{evaluate}}
%BeginExpansion
my=-nx+2m%
%EndExpansion
$

\subsection{Solution}

\begin{enumerate}
\item  The gradient of $L_{1}$ is $\frac{%
%TCIMACRO{\FORMULA{qm}{qm}{evaluate}}
%BeginExpansion
qm%
%EndExpansion
}{%
%TCIMACRO{\FORMULA{k}{k}{evaluate}}
%BeginExpansion
k%
%EndExpansion
}$; the gradient of $L_{2}$ should be $\frac{%
%TCIMACRO{\FORMULA{-qk}{-qk}{evaluate}}
%BeginExpansion
-qk%
%EndExpansion
}{%
%TCIMACRO{\FORMULA{m}{m}{evaluate}}
%BeginExpansion
m%
%EndExpansion
}$

\item  In the graph $L_{1}$ is in black colour; $L_{2}$ is in blue :

\FRAME{itbpFU}{3in}{2.0003in}{0in}{\Qcb{{}}}{}{}{\special{language
"Scientific Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth
0in;display "USEDEF";function \TEXUX{$f$};linecolor "black";linestyle
1;linethickness 2;pointstyle "point";function \TEXUX{$g$};linecolor
"blue";linestyle 1;linethickness 2;pointstyle "point";xmin "-5";xmax
"5";xviewmin "-5";xviewmax "5";yviewmin "-5";yviewmax
"5";viewset"XY";rangeset"X";phi 45;theta 45;plottype 4;constrained
TRUE;numpoints 49;axesstyle "normal";xis \TEXUX{g};var1name \TEXUX{$x$};}}

\item  \hyperref{Click here}{}{}{} to see the worked example.
\end{enumerate}

\end{document}