Draw specific image with TikZ

Question

I want to draw this image: I write this code, but I can't define mirror nodes based on nodes A1 ... A4.

How define nodes B1 ... B4 based on A1 ... A4?

\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usepackage{amsmath,amsfonts,amssymb}
\begin{document}
\begin{tikzpicture}[line cap=round]
% First, define nodes
\node[inner sep=0pt] (A1) at (0, 0) {};

\node[inner sep=0pt] (A2) at (1, 0) {};

\node[inner sep=0pt] (A3) at (1.5, 1.5) {};

\node[inner sep=0pt] (A4) at (-0.2, 1) {};
\draw [line width=2pt, -] (A1) -- (A2) -- (A3) -- (A4) -- (A1);
\end{tikzpicture}
\end{document}

In this case it‘s simple to calculate the required transformation for 4 x-coordinates by hand or head, place 4 more nodes and draw one more path. // You can also end the draw statement with cycle, instead of (A1), if you like: it will close the path. — MS-SPO, Apr 25 '23 at 03:48
Can you provide a more description title for your question? "How to draw this?" doesn't help people searching this site. — Werner, Apr 25 '23 at 17:36

Alain Matthes · Answer 1 · 2023-04-25T06:55:55.587

With a reflection and the macro \tkzDefPointsBy you can define easily $B1, B2, B3, B4$. You ajust the position with the coordinates of $I$ and $J$.

This is possible with only TikZ but if you want some other figures like this you can invest some time in the study of tkz-euclide.

\documentclass[border=5pt]{standalone}
\usepackage{tkz-euclide}
\usepackage{amsmath,amsfonts,amssymb}
\begin{document}
\begin{tikzpicture}[line cap=round,scale=2]
\tkzDefPoints{0/0/A1,1/0/A2,1.5/1.5/A3,-0.2/1/A4,2/0/I,2/2/J}
\tkzDefPointsByreflection = over I--J{B1,B2,B3,B4}
\tkzDrawPolygons(A1,A2,A3,A4 B1,B2,B3,B4)
% drawing
\tkzSetUpStyle[font=\footnotesize]{label style}
   \tkzLabelPointsleft
   \tkzLabelPointsright,font=\footnotesize
   \tkzMarkAngles[size=.3](A1,A4,A3 B1,B2,B3 B3,B4,B1)
   \tkzLabelAnglepos = 0.4{$r$}
   \tkzLabelAnglepos = 0.4{$t$}
   \tkzLabelAnglepos = 0.4{$s$}
   \tkzLabelSegmentright{$y$}
   \tkzLabelSegmentleft{$3y-8$}
\end{tikzpicture}
\end{document}

score 3 · Answer 2 · answered Apr 25 '23 at 04:53

Since coordinates have a somewhat fixed position once they are defined, you would need to transform (flip and shift) them manually (such as ([shift={(4, 0)}, xscale=-1]A1)). But you could create a macro to define them inside an already transformed scope like this nice answer suggests.

Apart from this, I would suggest that you really use \coordinates instead of \nodes to define the paths and use the line join option.

MWE:

\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[line join=round]
\newcommand{\definecoordinates}[1][A]{%
    % First, define coordinates
    \coordinate (#11) at (0, 0);

    \coordinate (#12) at (1, 0);

    \coordinate (#13) at (1.5, 1.5);

    \coordinate (#14) at (-0.2, 1); 
}
\begin{scope}
    \definecoordinates
    \draw[line width=2pt] (A1) -- (A2) -- (A3) -- (A4) -- cycle;
\end{scope}
\begin{scope}[shift={(4, 0)}, xscale=-1]
    \definecoordinates[B]
    \draw[line width=2pt] (B1) -- (B2) -- (B3) -- (B4) -- cycle;
\end{scope}
\end{tikzpicture}
\end{document}

score 3 · Answer 3 · answered Apr 25 '23 at 14:57

For comparison, here is a version in Metapost showing how to do reflection.

This is wrapped up with luamplib so you need to compile it with lualatex.

\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
beginfig(1);
path A, B;  
A = origin -- (32, -96) -- (128, -96) -- (144, 72) -- cycle;
A := A shifted 160 left;
B = A reflectedabout(up, down);
vardef add_angle_label(expr a, o, b, r, t) = 
    save arc; path arc; 
    arc = fullcircle scaled 2r rotated angle (a-o) shifted o cutafter (o..b);
    draw arc withcolor 3/4 red;
    label(t, beyond(o, point arctime 1/2 arclength arc of arc of arc, 6));
enddef;
vardef median(expr p) = save n; numeric n; n = length p; 
    origin for i=1 upto n: + point i of p scaled (1/n) endfor enddef;
vardef beyond(expr a, b, o) = save d; d = abs(b-a); (1+o/d)[a, b] enddef;
add_angle_label(point 1 of A, point 4 of A, point 3 of A, 10, "$r$");
add_angle_label(point 3 of B, point 4 of B, point 1 of B, 10, "$s$");
add_angle_label(point 1 of B, point 2 of B, point 3 of B, 10, "$t$");
forsuffixes $=A, B:
    pair m; m = median($);
    draw $ withcolor 1/2 blue;
    for i=1 upto 4:
        label("$" & str $ & "_" & decimal i & "$", beyond(m, point i of $, 8));
    endfor
endfor
label.urt ("$y$", point 1/2 of A);
label.ulft("$3y-8$", point 1/2 of B);
endfig;
\end{mplibcode}
\end{document}

Notes

The first <path> variable A is created like this:

A = origin -- (32, -96) -- (128, -96) -- (144, 72) -- cycle;

then shifted so it is the left of the origin (note that you have to use := to update it).

A := A shifted 160 left;

Then the second <path> variable B is created in one go:

B = A reflectedabout(up, down);

Then I've added a couple of useful macros:

add_angle_label creates an appropriate circular arc, draws it in red, and then adds the label t half way along it.
median gives you a weighted central point for any cyclic polygon path -- a bit more useful than center if the shape is irregular.
beyond(a, b, o) returns a <pair> that is o pt beyond b in the direction of a--b.

Finally the shapes and labels are drawn in a nested loop.

score 1 · Answer 4 · answered Apr 25 '23 at 15:23

Using the generalization of mirroring along an axis following my answer to Can we mirror a part in tikz ("axial symmetry", "reflection")?.

The Ai coordinates are defines as usual, the Bi are defined via the A nodes with an active transformations: xmirror = 2, i.e. mirroring at an axis that follows x = 2.

The rest of the diagram is then just drawing the polygons and marking lines, angles and vertices.

Code

\documentclass[tikz]{standalone}
\usetikzlibrary{angles, ext.transformations.mirror, quotes}
\tikzset{
  _pos xmirror/.style args={#1 = #2}{
    xmir #1/.style={#2={##1}}, xmir #2/.style={#1={##1}}},
  _pos xmirror/.list={
    right = left, above right = above left, below left = below right,
                  above       = above,      below      = below}} % not used
\begin{document}
\begin{tikzpicture}[angle eccentricity = 1, scale = 2]
\coordinate (A1) at (0, 0)
 coordinate (A2) at (1, 0)
 coordinate (A3) at (1.5, 1.5)
 coordinate (A4) at (-.2, 1);
% mirror coordinates at x = 2 and draw closed polygons
\foreach \i in {1,...,4} \coordinate(B\i) at ([xmirror = 2]A\i);
\draw[sharp cycle, samples at = {1, ..., 4}] foreach \p in {A, B} {plot (\p\x)};
% mark lines
\path (A1) to["$y$"   right] (A4)
      (B1) to["$3y-8$" left] (B4);
% mark angles
\scoped[inner sep = .15em, pics/angle/.append style = /tikz/draw]
  \pic["$r$" below right]  {angle = A1--A4--A3}
   pic["$s$", below left]  {angle = B3--B4--B1}
   pic["$t$", above right] {angle = B1--B2--B3};
% mark vertices
\foreach \n/\p in {1/left, 2/right, 3/right, 4/above left}
  \node[     \p] at (A\n) {$A_{\n}$}
   node[xmir \p] at (B\n) {$B_{\n}$};
\end{tikzpicture}
\end{document}

Draw specific image with TikZ

4 Answers4

Notes

Code

Output