Additional Practice Problems

\begin{document} \maketitle Tondeur's text does not have many easy, practice problems, similar to what you can expect on quizzes and tests. So here is a growing collection of problems to test your understanding of the material. You should also treat these problems as a practice quiz, so write your answers on scratch paper. Check your answers to the solutions . Then put them into your journal for future reference. \begin{enumerate} \item In the barycentric coordinates $ (a,b,c)$ relative to $\triangle ABC$ where does the line $ a = 0.3 $ cross $ (AB) $ ? \item Given $\triangle ABC$ with $(A'BC), (AB'C), (ABC')$. Let $ A' = -B +2C $ and $ B'= 0.5 A + 0.5 C $ find $ C'(AB) $ so that the three cevians are concurrent. \item Consider barycentric coordinates $ (a,b,c) $ relative to $ \triangle ABC $. Where does the line with equation $ 2b - c =0 $ cross $ (BC) $ ? \item Given four points $P_1, P_2, P_3, P_4 $ with $(P_1 P_2 P_3)$ and $(P_2 P_3 P_4)$, show that $\frac{P_1-P_2}{P_1-P_3} = \frac{P_4-P_2}{P_4-P_3} $ if and only if $P_1=P_4$. \end{enumerate} \end{document}