sandbox for activities

Author: annadavismath

SAND-0010/main.tex

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+\documentclass{ximera}
+\input{../preamble.tex}
+
+\title{Linear Combinations and Alternative Coordinate Systems} \license{CC BY-NC-SA 4.0}
+
+\begin{document}
+
+\begin{abstract}
+\end{abstract}
+\maketitle
+
+\begin{onlineOnly}
+\section*{Linear Combinations and Alternative Coordinate Systems}
+\end{onlineOnly}
+
+
+
+\section*{Explorations}
+
+\begin{exploration}\label{exp:coordSystemLinCombs}
+Use the interactive below to answer the questions
+% https://www.geogebra.org/classic/qw5dpmqq
+\begin{center}
+    \geogebra{qw5dpmqq}{800}{600}
+\end{center}
+\begin{question}
+    List the coordinates for each $P_i$ with respect to the given coordinate system.  Your coordinates should be of the form $(A\text{-coordinate}, B\text{-coordinate})$.
+    $$P_1=\left(\answer{1},\answer{1}\right)$$
+    $$P_2=\left(\answer{-2},\answer{0}\right)$$
+    $$P_1=\left(\answer{0},\answer{-1}\right)$$
+    $$P_1=\left(\answer{-2},\answer{3}\right)$$
+    $$P_1=\left(\answer{3},\answer{-2}\right)$$
+\end{question}
+
+\begin{question}
+Move point $B$ to coincide with $P_3$
+    List the coordinates for each $P_i$ with respect to the new coordinate system.  Your coordinates should be of the form $(A\text{-coordinate}, B\text{-coordinate})$.
+    $$P_1=\left(\answer{1},\answer{-1}\right)$$
+    $$P_2=\left(\answer{-2},\answer{0}\right)$$
+    $$P_1=\left(\answer{0},\answer{1}\right)$$
+    $$P_1=\left(\answer{-2},\answer{-3}\right)$$
+    $$P_1=\left(\answer{3},\answer{2}\right)$$
+    How do these coordinates compare to the coordinates in the previous question?  Explain why this is happening. (Hint: you can use the RESET button to return to the original coordinate system to compare.)
+\end{question}
+
+\begin{question}
+Press RESET to return to the original coordinate system.  Move point $A$ to coincide with $P_1$
+    List the coordinates for each $P_i$ with respect to the new coordinate system.  Your coordinates should be of the form $(A\text{-coordinate}, B\text{-coordinate})$.
+    $$P_1=\left(\answer{1},\answer{0}\right)$$
+    $$P_2=\left(\answer{-2},\answer{2}\right)$$
+    $$P_1=\left(\answer{0},\answer{-1}\right)$$
+    $$P_1=\left(\answer{-2},\answer{5}\right)$$
+    $$P_1=\left(\answer{3},\answer{-5}\right)$$
+    How do these coordinates compare to the coordinates in the original coordinate system?  Explain why this is happening. (Hint: you can use the reset button to return to the original coordinate system to compare.)
+\end{question}
+
+\begin{question}
+    Press RESET to return to the original coordinate system.  Express each $\overrightarrow{OP}_i$ as a linear combination of $\overrightarrow{OA}$ and $\overrightarrow{OB}$.
+$$\overrightarrow{OP}_1=\answer{1}\overrightarrow{OA}+\answer{1}\overrightarrow{OB}$$
+$$\overrightarrow{OP}_2=\answer{-2}\overrightarrow{OA}+\answer{0}\overrightarrow{OB}$$
+$$\overrightarrow{OP}_3=\answer{0}\overrightarrow{OA}+\answer{-1}\overrightarrow{OB}$$
+$$\overrightarrow{OP}_4=\answer{-2}\overrightarrow{OA}+\answer{3}\overrightarrow{OB}$$
+$$\overrightarrow{OP}_5=\answer{3}\overrightarrow{OA}+\answer{-2}\overrightarrow{OB}$$
+
+Discuss the relationship between your answers to the first question and your answers here.
+\end{question}
+
+\end{exploration}
+
+\end{document} 

sandbox.tex

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+\documentclass{xourse}
+
+\input{preamble.tex}
+
+ \title{Sandbox}
+
+\begin{document}
+\begin{abstract}
+\end{abstract}
+\maketitle
+
+
+\activity{SAND-0010/main}
+
+
+\end{document}