Tkz-euclide: Construct an orthogonal line

Question

I have a figure like the image:

Code:

\usepackage{tkz-euclide}
\usetikzlibrary{intersections,arrows.meta}
\usetkzobj{all}
\usetikzlibrary{patterns}
\pgfdeclarepatternformonly{my north east lines}{\pgfqpoint{-1pt}{-1pt}}{%
\pgfqpoint{8pt}{8pt}}{\pgfqpoint{7pt}{7pt}}%
{
  \pgfsetlinewidth{0.4pt}
  \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
  \pgfpathlineto{\pgfqpoint{7.1pt}{7.1pt}}
  \pgfusepath{stroke}
}



 \begin{figure}[t!]
    \centering
    %--------------------------
    \begin{tikzpicture}[>= {Stealth[scale=2.2,inset=0pt,angle'=20]}]  
      %Definindo os vertices
      %Eixo y
      \tkzDefPoint (0,0){A}
      \tkzDefPoint (-1.5,4){B}
      %Chao1
      \tkzDefPoint (0,0){A}
      \tkzDefPoint (6,2.25){D}
      %Chao1
      \tkzDefPoint (0,0){G}
      \tkzDefPoint (6,0){H}
      %Desenhando as retas/setas
      \draw (A) -- (D);
      \draw[->] (A) -- (B); 
      \draw[dashed] (G) -- (H);
      \tkzDrawArc[R with nodes, color=black](A,1cm)(H,D)
      \tkzLabelAngle[pos = 1.25](H,A,D){$\theta$}
\end{tikzpicture}
      \end{figure}    

How can I construct a second line which is orthogonal with the arrow, like this image:

Answer 1

If you reject the codes of the library calc and you want everything to be written in tkz-euclide, it is not valid to use the \draw sentences, here a similar code using pure coding in tikz-euclide,starting defining a point of reference and vectors from this, then calculate a second point B perpendicular,... in te code is explained... about the use of tikz euclide, as a package, limits the drawing to the set of its macros, instead basic tikz code that has huge drawing options.And for the language, I dont know French, but I know how to read mnemonics and fortunately this package has mnemonics in English and related to what they do.

RESULT:

MWE:

\documentclass[tikz,border=20pt]{standalone}
\usepackage{tkz-euclide}
\usetikzlibrary{patterns,arrows.meta}
\usetkzobj{all}

\pgfdeclarepatternformonly{my north east lines}{\pgfqpoint{-1pt}{-1pt}}{%
\pgfqpoint{8pt}{8pt}}{\pgfqpoint{7pt}{7pt}}%
{
  \pgfsetlinewidth{0.4pt}
  \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
  \pgfpathlineto{\pgfqpoint{7.1pt}{7.1pt}}
  \pgfusepath{stroke}
}
\begin{document}
    \begin{tikzpicture}
    %Definindo os vertices
    %%The best way to define Axis is using polar notation:
    \tkzDefPoint(0,0){O} %The reference point
    \tkzDefShiftPoint[O](0:5){Xo}% Axis X 
    \tkzDefShiftPoint[O](30:5){A} % Point A Vector

    %%Find a point B orthogonal to OA and with length 0.7 OA
    \tkzDefLine[perpendicular=through O.center,K=0.7](O,A) \tkzGetPoint{B}

    %%Find a point C linear 0.7 within line OB
    \tkzDefPointWith[linear,K=0.7](O,B)\tkzGetPoint{C}

    %%Find a point D orthogonal to OB with length -1 OA changes the direction 180 degrees
    \tkzDefLine[perpendicular=through C.center,K=-1](O,B) \tkzGetPoint{D}

    %%Find projection D' from point A in line C--D
    \tkzDefPointBy[projection=onto C--D](A) \tkzGetPoint{D'}

    %%Find projection Xi from point A in line O--Xo
    \tkzDefPointBy[projection=onto O--Xo](A) \tkzGetPoint{Xi}

    %Creation segments and labels
    %Mark and label angle
    \tkzMarkAngle[fill=blue!30,mkpos=1, size=0.7](Xo,O,A)
    \tkzLabelAngle(Xo,O,A){\large $\theta$} 
    \tkzMarkRightAngle[fill](A,O,B)
    \tkzMarkRightAngle[fill=blue,color=blue](D,C,O)
    \tkzMarkRightAngle[dashed](A,D',D)

    %Drawing modified style lines
    {%style only afects commands inside {}
        \tikzset{line style/.append style={->},>={Stealth[scale=2.2,inset=0pt,angle'=20]}} 
            \tkzDrawLine[add=0 and 20pt](O,A)
            \tkzDrawLine[add=0 and 20pt](O,B)   
    }
    %Drawing Standard lines
    \tkzDrawLine[color=blue](C,D')
    \tkzDrawSegments[dashed](A,D' O,Xi)

    %Drawing and label Points
    \tkzDrawPoints[color=blue,fill=blue,size=6pt](O,A,B,C,D,D')
    \tkzLabelPoints[color=blue,below=5pt,inner sep=0](O,A)
    \tkzLabelPoints[color=blue,above=5pt,inner sep=0](D,D')
    \tkzLabelPoints[color=blue,left=5pt,inner sep=0](B,C)
    \end{tikzpicture}

\end{document}

ANIMATION: obtained using Imagemagick converter (PDF to gif).

MWE:

% arara: pdflatex: {synctex: yes, action: nonstopmode}
% arara: animate: {density: 150, delay: 15 , other: -background white -alpha remove}
% arara: showanimate
\documentclass[tikz,border=5pt]{standalone}
\usepackage{tkz-euclide}
\usetikzlibrary{patterns,arrows.meta}
\usetkzobj{all}

\pgfdeclarepatternformonly{my north east lines}{\pgfqpoint{-1pt}{-1pt}}{%
    \pgfqpoint{8pt}{8pt}}{\pgfqpoint{7pt}{7pt}}%
{
    \pgfsetlinewidth{0.4pt}
    \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
    \pgfpathlineto{\pgfqpoint{7.1pt}{7.1pt}}
    \pgfusepath{stroke}
}
\begin{document}
    \foreach \X in {1,2,...,10,9,8,...,1}{
    \begin{tikzpicture}
    \pgfmathparse{int(\X*60/10)}
    \edef\ANGLE{\pgfmathresult}
    \tkzInit[xmin=-4,xmax=6,ymax=7, ymin=-2]
    \tkzClip
    %Definindo os vertices
    %%The best way to define Axis is using polar notation:
    \tkzDefPoint(0,0){O} %The reference point
    \tkzDefShiftPoint[O](0:5){Xo}% Axis X 
    \tkzDefShiftPoint[O](\ANGLE:5){A} % Point A Vector

    %%Find a point B orthogonal to OA and with length 0.7 OA
    \tkzDefLine[perpendicular=through O.center,K=0.7](O,A) \tkzGetPoint{B}

    %%Find a point C linear 0.7 within line OB
    \tkzDefPointWith[linear,K=0.7](O,B)\tkzGetPoint{C}

    %%Find a point D orthogonal to OB with length -1 OA changes the direction 180 degrees
    \tkzDefLine[perpendicular=through C.center,K=-1](O,B) \tkzGetPoint{D}

    %%Find projection D' from point A in line C--D
    \tkzDefPointBy[projection=onto C--D](A) \tkzGetPoint{D'}

    %%Find projection Xi from point A in line O--Xo
    \tkzDefPointBy[projection=onto O--Xo](A) \tkzGetPoint{Xi}

    %Creation segments and labels
    %Mark and label angle
    \tkzMarkAngle[fill=blue!30,mkpos=1, size=0.7](Xo,O,A)
    \tkzLabelAngle[pos=1.5](Xo,O,A){\large $\theta$=\ANGLE} 
    \tkzMarkRightAngle[fill](A,O,B)
    \tkzMarkRightAngle[fill=blue,color=blue](D,C,O)
    \tkzMarkRightAngle[dashed](A,D',D)

    %Drawing modified style lines
    {%style only afects commands inside {}
        \tikzset{line style/.append style={->},>={Stealth[scale=2.2,inset=0pt,angle'=20]}} 
        \tkzDrawLine[add=0 and 20pt](O,A)
        \tkzDrawLine[add=0 and 20pt](O,B)   
    }
    %Drawing Standard lines
    \tkzDrawLine[color=blue](C,D')
    \tkzDrawSegments[dashed](A,D' O,Xi)

    %Drawing and label Points
    \tkzDrawPoints[color=blue,fill=blue,size=6pt](O,A,B,C,D,D',Xi)
    \tkzLabelPoints[color=blue,below=5pt,inner sep=0](O,A)
    \tkzLabelPoints[color=blue,above=5pt,inner sep=0](D,D')
    \tkzLabelPoints[color=blue,left=5pt,inner sep=0](B,C)
    \end{tikzpicture}
}

\end{document}

Answer 2

Here is a solution TikZ users who are not good at French. All you have to do is to look at the example in the pgfmanual at the top of p. 145.(Sorry to be so rude, but I guess some of those defending the French tkz-euclide package, which is undoubtedly great except for the accesibility of manual, would not be too excited if the pgfmanual was written in German. I do not want to provoke anyone here, just explain why I am not able to present a tkz-euclide based solution.)

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tkz-euclide}
\usetikzlibrary{arrows.meta}
\usetkzobj{all}

\begin{document}
    \begin{tikzpicture}[>= {Stealth[scale=2.2,inset=0pt,angle'=20]}]  
      %Definindo os vertices
      %Eixo y
      \tkzDefPoint (0,0){A}
      \tkzDefPoint (-1.5,4){B}
      %Chao1
      \tkzDefPoint (0,0){A}
      \tkzDefPoint (6,2.25){D}
      %Chao1
      \tkzDefPoint (0,0){G}
      \tkzDefPoint (6,0){H}
      %Desenhando as retas/setas
      \draw (A) -- (D);
      \draw[->] (A) -- (B); 
      \draw[dashed] (G) -- (H);
      \tkzDrawArc[R with nodes, color=black](A,1cm)(H,D)
      \tkzLabelAngle[pos = 1.25](H,A,D){$\theta$}
      % almost 1:1 copy of the example in the pgfmanual at the top of p. 145
      \coordinate (I) at ($ (A)!0.9!(B) $);
      \coordinate (J) at ($ (I)!6cm!90:(A) $);
      \draw (I) -- (J);
\end{tikzpicture}
\end{document}    

Answer 3

In order to make my explanation clear to everyone, I drew the points as blue cross and displayed the name of the perpendicular called delta.

On your figure, point B is the end of the arrow. To draw a half-line with this origin below the arrow, we can use the macro \tkzDefBarycentricPoint which allows to build the barycenter of several points, here of the two points A and B. To place it in the same place as @marmot do (at 9/10 of the segment), we will assign a weight of 9 to point B and a weight of 1 to point A. Let us call this point B'. We have OB' =1/10( 9 OB + 1 OA). (Sorry, I don't know how to write vectors with the tex.exchange editor)

To draw a line, whatever its perpendicular or parallel, the principle of tkz-euclide macros is to define first the 2 points necessary to build this line.

here, the macro \tkzDefLine[perpendicular=through B'](B,A) \tkzGetPoint{B''} defines the second point from perpendicular (called delta) to right (AB) through (B'). Let's call this second point B''.

Since you want to draw a half-line of origin B', we will not extend the representation of the line using the parameter add= 0, but we will extend it after point B'' of half the segment [B' B''] with add=.5. \tkzDrawLine[add = 0 and .5,end = $(\delta)$](B',B''').

\documentclass{article}
\usepackage{tkz-euclide}
\usetikzlibrary{intersections,arrows.meta}
\usetkzobj{all}

\pgfdeclarepatternformonly{my north east lines}{\pgfqpoint{-1pt}{-1pt}}{%
\pgfqpoint{8pt}{8pt}}{\pgfqpoint{7pt}{7pt}}%
{
  \pgfsetlinewidth{0.4pt}
  \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
  \pgfpathlineto{\pgfqpoint{7.1pt}{7.1pt}}
  \pgfusepath{stroke}
}

\begin{document}
 \begin{figure}[t!]
    \centering
%--------------------------
    \begin{tikzpicture}[>= {Stealth[scale=2.2,inset=0pt,angle'=20]}]  
      %Definindo os vertices
      %Eixo y
      \tkzDefPoint (0,0){A}
      \tkzDefPoint (-1.5,4){B}
      %Chao1
      \tkzDefPoint (0,0){A}
      \tkzDefPoint (6,2.25){D}
      %Chao1
      \tkzDefPoint (0,0){G}
      \tkzDefPoint (6,0){H}
      %Desenhando as retas/setas
      \draw (A) -- (D);
      \draw[->] (A) -- (B); 
      \draw[dashed] (G) -- (H);
      \tkzDrawArc[R with nodes, color=black](A,1cm)(H,D)
      \tkzLabelAngle[pos = 1.25](H,A,D){$\theta$}
      \tkzDefBarycentricPoint(A=1,B=9)
      \tkzGetPoint{B'}
      \tkzDefLine[perpendicular=through B'](B,A) \tkzGetPoint{B''}
      %\tkzDefLine[orthogonal=through B'](B,A) \tkzGetPoint{B''}
      \tkzDrawLine[add = 0 and .5,end = $(\delta)$](B',B'')
      \tkzDrawPoints[shape=cross,size=20,color=blue](A,D,B,B',B'')
      \tkzLabelPoints[below left](A,B,B')
      \tkzLabelPoints(D,B'')
\end{tikzpicture}
      \end{figure}  
\end{document}

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