Square Pyramid -- Distances

Submitted by ladislav.foltyn on Wed, 05/01/2019 - 15:58
Project ID: 
5000000052
Accepted: 
SubArea: 
Metric properties
Template: 
B
Question: 
The base ABCD of a square pyramid ABCDV has an edge of 6cm. The height of the pyramid is 8cm. Let S be the midpoint of the base, P the midpoint of the edge AV, and Q the midpoint of the edge CV (see the picture). Find the distance between
Question Row 1: 
\ifen the point A and the point S \fi \ifcs bodem A a bodem S \fi \ifpl punktem A i punktem S \fi \ifsk bodom A bodom S \fi \ifes el punto A y el punto S \fi
Answer Row 1: 
322cm, 4cm, *32cm, 82cm
Question Row 2: 
\ifen the point P and the point Q \fi \ifcs bodem P a bodem Q \fi \ifpl punktem P i punktem Q \fi \ifsk bodom P bodom Q \fi \ifes el punto P y el punto Q \fi
Answer Row 2: 
*32cm, 8cm, 34cm, 73cm
Question Row 3: 
\ifen the point V and the point A \fi \ifcs bodem V a bodem A \fi \ifpl punktem V i punktem A \fi \ifsk bodom V bodom A \fi \ifes el punto V y el punto A \fi
Answer Row 3: 
322cm, 4cm, 32cm, *82cm
Question Row 4: 
\ifen the point P and the line VS \fi \ifcs bodem P a přímkou VS \fi \ifpl punktem P i prostą VS \fi \ifsk bodom P a priamkou VS \fi \ifes el punto P y la recta VS \fi
Answer Row 4: 
*322cm, 8cm, 73cm, 82cm
Question Row 5: 
\ifen the point V and the line BC \fi \ifcs bodem V a přímkou BC \fi \ifpl punktem V i prostą BC \fi \ifsk bodom V a priamkou BC \fi \ifes el punto V y la recta BC \fi
Answer Row 5: 
32cm, 4cm, *73cm, 82cm
Question Row 6: 
\ifen the point B and the line PQ \fi \ifcs bodem B a přímkou PQ \fi \ifpl punktem B i prostą PQ \fi \ifsk bodom B a priamkou PQ \fi \ifes el punto B y la recta PQ \fi
Answer Row 6: 
5cm, *34cm, 73cm, 82cm
Question Row 7: 
\ifen the line $AC$ and the line $PQ$ \fi \ifcs přímkou $AC$ a přímkou $PQ$ \fi \ifpl prostą $AC$ i prostą $PQ$ \fi \ifsk bodom $AC$ a priamkou $PQ$ \fi \ifes la recta $AC$ y la recta $PQ$ \fi
Answer Row 7: 
323cm, *4cm, 32cm, 6cm
Question Row 8: 
\ifen the point Q and the plane ABC \fi \ifcs bodem Q a rovinou ABC \fi \ifpl punktem Q i płaszczyzną ABC \fi \ifsk bodom Q a rovinou ABC \fi \ifes el punto Q y el plano ABC \fi
Answer Row 8: 
322cm, *4cm, 6cm, 8cm
Tex: 
% tiket 33346 \let\oldQuestion\Question \def\Question{ \begin{minipage}[t]{0.6\linewidth} \leavevmode \oldQuestion \end{minipage} \hfill \begin{minipage}[t]{0.35\linewidth} \leavevmode \kern -30pt \obrMsr[x=1.5cm,y=1.5cm,z=0.3cm]{-1}2{-1}2 { \footnotesize \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 (V) at (0.6,1.5,1); \coordinate (P) at ($(A)!0.5!(V)$); \coordinate (Q) at ($(C)!0.5!(V)$); \draw[thick,dashed] (A) -- (D) node [yshift=4pt,xshift=-6pt]{$D$} -- (C) node [yshift=-5pt,xshift=5pt]{$C$}; \draw[dashed] (A) -- (C); \draw[dashed] (B) -- (D); \draw (0.6,0,1) node [below,xshift=-2pt,yshift=1pt]{$S$}; \draw[thick] (A) node [yshift=-5pt,xshift=-5pt]{$A$} -- (B) node [yshift=-6pt,xshift=3pt]{$B$} --(C); \draw[thick] (A) -- (V) node [above]{$V$}; \draw[thick] (B) -- (V); \draw[thick] (C) -- (V); \draw[thick,dashed] (D) -- (V); \draw[dashed] (0.6,0,1) -- (V); \begin{scope}[thick] \obrKrizek[2pt]{P}{above left}{P} \obrKrizek[2pt]{Q}{above right}{Q} \end{scope} } \end{minipage} \kern -20pt} \MsrTabulka[0pt]{0.4\linewidth}{0.6\linewidth} \pocetsloupcu{4}