How can I draw the attached picture in LaTeX?

Question

How can I draw the attached picture in LaTeX?

Answer 1

Just about does it...

\documentclass[tikz,border=5]{standalone}
\usetikzlibrary{intersections}
\begin{document}
\begin{tikzpicture}[dot/.style={insert path={ circle [radius=.05] }},
  line cap=round, line join=round, >=stealth]
\draw (0,2) -- (4,4)
  coordinate [pos=0.125] (A) coordinate [pos=0.5] (B) coordinate [pos=0.875] (C);

\draw (0,0) coordinate (O) -- (4,0) coordinate (O')
  coordinate [pos=0.2] (D) coordinate [pos=0.5] (E) coordinate [pos=0.8] (F);

\foreach \x/\y/\z in {A/E/F, B/D/F, C/D/E}{
  \draw [name path global=\x\y, blue!75!black] (\x) -- (\y);
  \draw [name path global=\x\z, blue!75!black] (\x) -- (\z); 
}

\foreach \x/\y/\z in {AE/BD/P, AF/CD/Q, BF/CE/R}
  \path [name intersections={of/.expanded=\x\space and \y, name=i}] 
    (i-1) coordinate (\z);

\draw [thick, orange, dashed, shorten >=-1cm, shorten <=-1cm] (P) -- (R);

\foreach \n in {A, B, C} \fill (\n) [dot] node [above] {\n};
\foreach \n in {D, E, F} \fill (\n) [dot] node [below] {\n};
\foreach \n/\a in {P/340, Q/280, R/330}
  \fill (\n) [dot] node [blue!75!black, anchor=\a] {\n};

\draw [ultra thick, ->, shorten >=-.125cm, red] (O) -- (O');
\draw [ultra thick, ->, red] (D) -- ++(0,3);
\end{tikzpicture}
\end{document}

Answer 2

I agree with the comments of the users, certainly more skilled than me, but I answer the same because it might be useful to others, especially the use of intersections and macro definitions.

You have to set the macro \a, \b, \c, \d, \e, \f to the x value you want, then the macro \m \q respectively to the upper line slope and intercept.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{intersections}

\begin{document}
\begin{tikzpicture}[extended line/.style={shorten >=-#1,shorten <=-#1}, extended line/.default=1cm]
\pgfmathsetmacro\d{0}
\pgfmathsetmacro\e{2}
\pgfmathsetmacro\f{4}
\pgfmathsetmacro\m{0.4}
\pgfmathsetmacro\q{3}
\pgfmathsetmacro\a{-1}
\pgfmathsetmacro\b{2}
\pgfmathsetmacro\c{5}

\coordinate[label=above:$A$](A)at(\a,\m*\a+\q);
\coordinate[label=above:$B$](B)at(\b,\m*\b+\q);
\coordinate[label=above:$C$](C)at(\c,\m*\c+\q);
\coordinate[label=below:$D$](D)at(\d,0);
\coordinate[label=below:$E$](E)at(\e,0);
\coordinate[label=below:$F$](F)at(\f,0);

\draw[blue, name path=A--E](A)--(E);
\draw[blue, name path=B--D](B)--(D);
\draw[blue, name path=A--F](A)--(F);
\draw[blue, name path=C--D](C)--(D);
\draw[blue, name path=B--F](B)--(F);
\draw[blue, name path=C--E](C)--(E);

\path [name intersections={of=A--E and B--D,by=P}];
\path [name intersections={of=A--F and C--D,by=Q}];
\path [name intersections={of=B--F and C--E,by=R}];
\node[blue, above]at(P){$P$};
\node[blue, above]at(Q){$Q$};
\node[blue, above]at(R){$R$};

\draw [extended line=0.5cm] (A)--(B)--(C);
\draw [extended line=0.5cm] (D)--(E)--(F);
\draw [extended line=0.5cm, red , dashed] (P)--(Q)--(R);

\draw[red, ->] (\d-1,0)--(\f+1,0);
\draw[red, ->] (0,-1)--(0,\c);

\fill (A)circle(2pt) (B)circle(2pt) (C)circle(2pt) (D)circle(2pt) (E)circle(2pt) (F)circle(2pt);
\fill[blue] (P)circle(2pt) (Q)circle(2pt) (R)circle(2pt);
\end{tikzpicture}
\end{document}