Cube -- Distances II

Submitted by ladislav.foltyn on Fri, 05/10/2019 - 21:27
Project ID: 
5000000059
Accepted: 
SubArea: 
Metric properties
Template: 
B
Question: 
The cube ABCDEFGH shown in the picture has edges of length 12cm. Let K be the midpoint of the edge EF and let L be the midpoint of the edge GH. Find the distance between
Question Row 1: 
\ifen the lines AB and CD: \fi \ifcs přímkami AB a CD: \fi \ifpl prostymi AB i CD: \fi \ifsk priamkami AB a CD: \fi \ifes las rectas AB y CD: \fi
Answer Row 1: 
*{12cm}, {122cm}, {123cm}, {126cm}
Question Row 2: 
\ifen the lines AB and KL: \fi \ifcs přímkami AB a KL: \fi \ifpl prostymi AB i KL: \fi \ifsk priamkami AB a KL: \fi \ifes las rectas AB y KL: \fi
Answer Row 2: 
{6cm}, {62cm}, {63cm}, *{12cm}
Question Row 3: 
\ifen the lines AB and GL: \fi \ifcs přímkami AB a GL: \fi \ifpl prostymi AB i GL: \fi \ifsk priamkami AB a GL: \fi \ifes las rectas AB y GL: \fi
Answer Row 3: 
{12cm}, *{122cm}, {123cm}, {126cm}
Question Row 4: 
\ifen the lines AB and HK: \fi \ifcs přímkami AB a HK: \fi \ifpl prostymi AB i HK: \fi \ifsk priamkami AB a HK: \fi \ifes las rectas AB y HK: \fi
Answer Row 4: 
{6cm}, {62cm}, {63cm}, *{12cm}
Question Row 5: 
\ifen the line AB and the plane KFC: \fi \ifcs přímkou AB a rovinou KFC: \fi \ifpl prostą AB i płaszczyzną KFC: \fi \ifsk priamkou AB a rovinou KFC: \fi \ifes la recta AB y el plano KFC: \fi
Answer Row 5: 
{3cm}, {6cm}, *{62cm}, {63cm}
Question Row 6: 
\ifen the line AB and the plane DCL: \fi \ifcs přímkou AB a rovinou DCL: \fi \ifpl prostą AB i płaszczyzną DCL: \fi \ifsk priamkou AB a rovinou DCL: \fi \ifes la recta AB y el plano DCL: \fi
Answer Row 6: 
*{12cm}, {122cm}, {123cm}, {126cm}
Tex: 
% tiket 33041 \let\oldQuestion\Question \def\Question{ \begin{minipage}[t]{0.6\linewidth} \leavevmode \oldQuestion \end{minipage} \hfill \begin{minipage}[t]{0.35\linewidth} \leavevmode \kern -20pt \obrMsr[x=1.5cm,y=1.5cm,z=0.2cm]{-1}2{-1}2 { \pgfmathsetmacro{\cubex}{1} \pgfmathsetmacro{\cubey}{1} \pgfmathsetmacro{\cubez}{2} \coordinate (A) at (0,0,0); \coordinate (B) at (\cubex,0,0); \coordinate (C) at (\cubex.2,0,\cubez); \coordinate (D) at (0.2,0,\cubez); \coordinate (E) at (0,\cubey,0); \coordinate (F) at (\cubex,\cubey,0); \coordinate (G) at (\cubex.2,\cubey,\cubez); \coordinate (H) at (0.2,\cubey,\cubez); \coordinate (K) at ($(E)!0.5!(F)$); \coordinate (L) at ($(H)!0.5!(G)$); \draw[thick,dashed] (A) -- (D) node [yshift=-6pt,xshift=3pt]{$D$} -- (C) node [yshift=-5pt,xshift=5pt]{$C$}; \draw[thick,dashed] (D) -- (H); \draw[thick] (A) node [yshift=-5pt,xshift=-5pt]{$A$} -- (B) node [yshift=-6pt,xshift=3pt]{$B$} -- (F) node [yshift=-6pt,xshift=6pt]{$F$}-- (E) node [yshift=6pt,xshift=-3pt]{$E$} -- cycle; \draw[thick] (B) -- (C) -- (G) -- (F); \draw[thick] (G) node [yshift=6pt,xshift=3pt]{$G$} -- (H) node [yshift=6pt,xshift=-3pt]{$H$} -- (E); \begin{scope}[red,thick] \obrKrizek[2pt]{K}{below right}{K} \obrKrizek[2pt]{L}{above}{L} \end{scope} } \end{minipage}} \MsrTabulka[2pt]{0.35\linewidth}{0.55\linewidth} \pocetsloupcu{4}