[Tex/LaTex] Shift entire TikZ-picture vertically into part of align environment

tikz-pgf

I am trying to move a TikZ-picture upward so that it eliminates the amount of space taken up for my solution. How can I move the TikZ-picture upward (just a bit) into the align-environment?
FYI, the following is the exam problem.

"The midpoint of the line segment from $(-2,1)$ to a point $P$ is $(1, -1)$. Determine the coordinates of $P$."

The following is my solution to the exam problem.

Let $P = (x,y)$. We need to find $x$ and $y$. We have
\begin{align*}
\text{Midpoint} = \biggl( \frac{-2 + x}{2} , \frac{1 + y}{2} \biggr)
\quad   &\implies \quad
(1,-1) = \biggl( \frac{-2 + x}{2} , \frac{1 + y}{2} \biggr)\\
&\implies \quad
\begin{dcases}
    1 = \frac{-2 + x}{2}\\
    -1 = \frac{1 + y}{2}
\end{dcases}\\
&\implies \quad
\begin{dcases}
    2 = -2 + x\\
    -2 = 1 + y
\end{dcases}
\quad \implies \quad
\begin{dcases}
    x = 4\\
    y = -3.
\end{dcases}
\end{align*}
%\begin{minipage}[t]{5cm}{        %DO I NEED THIS?
\begin{tikzpicture}[>=latex',scale=0.5]
% Draw grid lines
\draw[help lines] (-2.5,-3.5) grid (4.5,1.5);
% Draw x-axis
\draw[very thick,->] (-3,0) -- (5.5,0)
    node[right] {\large $x$}; 
% Draw y-axis
\draw[very thick, ->] (0,-4) -- (0,2.5) 
node[above] {\large $y$};
% Special points
\node[above, fill=SolutionColor] at (-2,1) {$(-2,1)$};
\fill (-2,1) circle (4pt);
\node[right, fill=SolutionColor] at (1.5,-1) {$(1,-1)$};
\fill (1,-1) circle (4pt);
\node[right, fill=SolutionColor] at (4,-3) {$P$};
\draw (-2,1) -- (1,-1) -- (4,-3);
\fill[red] (4,-3) circle (4pt);
\end{tikzpicture}
%\end{minipage}%    DO I NEED THIS?

enter image description here

Best Answer

This is a job for Martin Scharrer's excellent adjustbox package: It allows (among many other things) to trim the top off a box (which can contain, among many other things, a tikzpicture), so its official height is smaller than the actual height of the content.

If you wrap your tikzpicture in \begin{adjustbox}{trim=0 0 0 2.5cm} ... \end{adjustbox}, you'll get

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{arrows}
\usepackage{amsmath}
\usepackage{mathtools}
\usepackage{adjustbox}

\begin{document}
Let $P = (x,y)$. We need to find $x$ and $y$. We have
\begin{align*}
\text{Midpoint} = \biggl( \frac{-2 + x}{2} , \frac{1 + y}{2} \biggr)
\quad   &\implies \quad
(1,-1) = \biggl( \frac{-2 + x}{2} , \frac{1 + y}{2} \biggr)\\
        &\implies \quad
\begin{dcases}
    1 = \frac{-2 + x}{2}\\
    -1 = \frac{1 + y}{2}
\end{dcases}\\
        &\implies \quad
\begin{dcases}
    2 = -2 + x\\
    -2 = 1 + y
\end{dcases}
\quad \implies \quad
\begin{dcases}
    x = 4\\
    y = -3.
\end{dcases}
\end{align*}

\begin{adjustbox}{trim=0 0 0 2.5cm}%
\begin{tikzpicture}[>=latex',scale=0.5]
% Draw grid lines
\draw[help lines] (-2.5,-3.5) grid (4.5,1.5);
% Draw x-axis
\draw[very thick,->] (-3,0) -- (5.5,0)
    node[right] {\large $x$}; 
% Draw y-axis
\draw[very thick, ->] (0,-4) -- (0,2.5) 
node[above] {\large $y$};
% Special points
\node[above, fill=white] at (-2,1) {$(-2,1)$};
\fill (-2,1) circle (4pt);
\node[right, fill=white] at (1.5,-1) {$(1,-1)$};
\fill (1,-1) circle (4pt);
\node[right, fill=white] at (4,-3) {$P$};
\draw (-2,1) -- (1,-1) -- (4,-3);
\fill[red] (4,-3) circle (4pt);
\end{tikzpicture}
\end{adjustbox}
\end{document}

Related Solutions

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

A solution which allows to draw intersection segments of any two intersections is available as tikz library fillbetween.

This library works as general purpose tikz library, but it is shipped with pgfplots and you need to load pgfplots in order to make it work:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}];

\end{tikzpicture}

\end{document}

enter image description here

The key intersection segments is described in all detail in the pgfplots reference manual section "5.6.6 Intersection Segment Recombination"; the key idea in this case is to

create a temporary path temp1 which is the first intersection segment of red and blue, more precisely, it is the first intersection segment in the Left argument in red and blue : red. This path is drawn as thin black path. Substitute its \draw statement by \path to make it invisible.
Compute the desired intersection segment by intersecting temp1 and green and use the correct intersection segment. By trial and error I figured that it is the third segment of path temp1 which is written as L3 (L = left argument in temp1 and green and 3 means third segment of that path).

The argument involves some trial and error because fillbetween is unaware of the fact that end and startpoint are connected -- and we as end users do not see start and end point.

Note that you can connect these path segments with other paths. If such an intersection segment should be the continuation of another path, use -- as before the first argument in sequence. This allows to fill paths segments:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,fill=blue,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}]  
    [intersection segments={of=temp1 and green, sequence={--R2}}]
;

\end{tikzpicture}

\end{document}

enter image description here

[Tex/LaTex] Vertically shift down an edge

For example, the arrow can be shifted the following way. As anchor point for the shift, the example uses the north * anchors, to avoid a slanted line because of the different heights of the nodes.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc, arrows}

\begin{document}

\begin{tikzpicture}[
  >=latex',
]
  \draw
    (0,0) -- (10,0)

    \foreach \x in {0,2,4,7,9} {
      (\x cm,3pt) -- (\x cm,-3pt)
    }

    % draw nodes
    (0,0) node[below=3pt](A) {$ 0 $}
    (1,0) node[above=3pt] {$ Y_{i1} $}

    (2,0) node[below=3pt](C) {$ t_{i1} $}
    (3,0) node[above=3pt] {$ Y_{i2} $}

    (4,0) node[below=3pt](E) {$ t_{i2} $}
    (5.5,0) node[above=3pt] {$ Y_{i3} $}

    (7,0) node[below=3pt](G) {$ t_{i3} $}
    (8,0) node[above=3pt] {$ Y_{i3} $}

    (9,0) node[below=3pt](I) {$ t_{i4} $}
  ;

  %\draw[latex'-latex'] (A) -- (C);
  \draw[<->] ($(A.north east) - (0, 1em)$) -- ($(C.north west) - (0, 1em)$);
  \draw[<->] (C) -- (E);
  \draw[<->] (E) -- (G);

\end{tikzpicture}
\end{document}

If you want to correct the first arrow and move the left side down to get a horizontal line, then this can be achieved much easier via a \vphantom:

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

\begin{document}

\begin{tikzpicture}[
  >=latex',
]
  \draw
    (0,0) -- (10,0)

    \foreach \x in {0,2,4,7,9} {
      (\x cm,3pt) -- (\x cm,-3pt)
    }

    % draw nodes
    (0,0) node[below=3pt](A) {$ 0\vphantom{t_{i1}} $}
    % Now node A has the same height and depth as node C
    (1,0) node[above=3pt] {$ Y_{i1} $}

    (2,0) node[below=3pt](C) {$ t_{i1} $}
    (3,0) node[above=3pt] {$ Y_{i2} $}

    (4,0) node[below=3pt](E) {$ t_{i2} $}
    (5.5,0) node[above=3pt] {$ Y_{i3} $}

    (7,0) node[below=3pt](G) {$ t_{i3} $}
    (8,0) node[above=3pt] {$ Y_{i3} $}

    (9,0) node[below=3pt](I) {$ t_{i4} $}
  ;

  \draw[<->] (A) -- (C);
  \draw[<->] (C) -- (E);
  \draw[<->] (E) -- (G);

\end{tikzpicture}
\end{document}

Best Answer

Related Solutions

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

[Tex/LaTex] Vertically shift down an edge

Related Question