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Name (Last, First): $\underline{\hspace{3in}}$ \hfill Student ID: $\underline{\hspace{2in}}$

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{\small
  \href{\myurl}{Dror Bar-Natan}:
  \href{\myurl/classes/}{Classes}:
  \href{\myurl/classes/\#1415}{2014-15}:
  \href{\myurl/classes/15-475-ProblemSolving}{MAT 475 Problem Solving Seminar}:
  \hfill\url{http://drorbn.net/15-475}
}

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{\large\bf Quiz 2} ``Draw a Figure'', January 20, 2015. You have 30 minutes to solve as much as you can of the following problems. Please write on both sides of the page. \hfill {\bf Good Luck!}

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\noindent{\bf Problem 1} (Larson's problem 1.2.6). Let $ABC$ be an acute-angled triangle (all angles below $90^\circ$), and let $D$ be on the interior of the segment $AB$. Describe how one can find points $E$ on $AC$ and $F$ on $BC$ such that the triangle $DEF$ will have the minimal possible perimeter.

\noindent{\bf Problem 2} (Larson's problem 1.2.9). Let $0<a<b$ be real numbers. If two points are selected at random from a straight line segment of length $b$, what is the probability that the distance between them is at least $a$?

\noindent{\bf Problem 3} (no credit). Use the back of this quiz to draw a figure of something interesting. The best figures will be placed somewhere on this class' web site.

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Problem 3 solution by Alessandra:

\[ \includegraphics[width=7.5in]{Quiz2Problem3ByAlessandra.jpg} \]

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Problem 3 solution by Shola:

\[\includegraphics[width=3.72in]{Quiz2Problem3ByShola.jpg} \]

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