# Create tick marks on a segment

The idea is to reproduce the figure such that point U has abscissa -5/7 and point P has root 13. My practice of Metapost is not sufficient to finish the figure.

   \documentclass[border=5mm]{standalone}
\usepackage{luatex85}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
beginfig(1);
u  = 1.5cm;
z0 = (0,0);
z1 = (-2u,0);
z2 = (4u,0);
z3 = (u,0);
z4 = (sqrt(13)*u,0);
z5 = ((-5/7)*u,0);
z6 = (0,-3*u);
z7 = (2u,-3u);
z8 = (2u,0);

path q;
q = unitsquare scaled 5;

picture X;
X = image(
drawoptions(withpen pencircle scaled 1.25 withcolor 1/4[blue, white]);
draw (left--right) scaled 2;
draw (down--up) scaled 2;
drawoptions();
);

draw X shifted z0;
draw X shifted z3;
draw X shifted z4;
draw X shifted z5;

fill q rotated 180 shifted z8 withcolor 1/3[green, white];
draw q rotated 180 shifted z8 ;

fill q rotated -90 shifted z0 withcolor 1/3[green, white];
draw q rotated -90 shifted z0 ;

fill q rotated 90  shifted z7 withcolor 1/3[green, white];
draw q rotated 90 shifted z7 ;

fill q  shifted z6 withcolor 1/3[green, white];
draw q  shifted z6 ;

draw z0 -- z7 withcolor 1/2[red, white];

draw z1 -- z2;
path rectangle;
rectangle = z0 -- z6 -- z7 -- z8 -- cycle;
draw rectangle;

label.lrt("$U$",z5);
label.top("$O$",z0 + (0,3));
label.top("$I$",z3 + (0,3));
label.top("$P$",z4 + (0,3));
label.lft("3",0.5[z0, z6]) withcolor 1/2[red, black];
label.bot("2",0.5[z6, z7]) withcolor 1/2[red, black];
label.bot("$-1$", (-u,0));

path r;
r = fullcircle scaled 7.211102551u;

draw subpath (6.5, 8) of r;
draw (-0.8)[z0, point 2.35 of rectangle] -- 1.8[z0, point 2.35 of rectangle]  withcolor 1/2[blue, white];
endfig;
\end{mplibcode}
\end{document}


• Sorry, but it is not clear to me what you want to achieve. Aren't the coordinates for U and P already correct? Sep 22 at 19:16
• @Jasper Hello, my problem is not the positioning of the points P and Q whose abscissas were calculated with the theorems of Thales and Pythagoras but rather on how to draw the blue line and be able to divide it into seven equal segments. Sep 24 at 12:14
• I see. But then, I fear that you need to help me understand how the blue line and the two red lines in the reference picture are defined. Sep 24 at 12:18
• I don't know, but all you have to do is draw one arbitrarily. Sep 24 at 12:50