How to extend a line with a specific proportion?

Question

Given point $A$ and point $B$, on the one hand, I would like to get a point that is an affine combination of $A$ and $B$, for example $1.2A-0.2B$, on the other hand, I would like to get the coordinate of the intersection point of $AB$'s extended line and $CD$.

The MWE is as follows.

\documentclass[notitlepage, 12pt]{amsart}
\usepackage{amsthm, amsmath, amsaddr, amssymb, graphicx, dsfont,}
 \usepackage[dvipsnames]{xcolor}
\renewcommand{\baselinestretch}{1.2}
  \usepackage{tikz}
  \usetikzlibrary{calc,intersections,through,backgrounds}
   \usepackage{pgfplots} 
   \usepackage[capposition=bottom]{floatrow}
   \usepackage{float}
   \pgfplotsset{compat=1.18}
\begin{document}
\thispagestyle{empty}
\begin{figure}[H]
\centering

\begin{tikzpicture}[xscale=18,yscale=18]


 \coordinate (A) at (0.2,0.3);

 \coordinate (B) at (0.3,0.2);

 \coordinate (C) at (0.4,0.2);

\coordinate (D) at (0.4,0.5);




    \end{tikzpicture}

   \caption{}

  \end{figure}




  \end{document}

@cfr I added a MWE. By the way, how can I add the code quickly? I have to add several spaces before each line manually... — Ypbor, Mar 06 '24 at 04:08
point C and D are at the same coordinate - how do you draw a line through them — js bibra, Mar 06 '24 at 04:17
Please limit your question to one question. If you want a combination of two coordinates, see my answer below. If you want the intersection point of two lines, use the intersections library. — Sandy G, Mar 06 '24 at 04:22
for extending a combination of coordinates see my answer here using tkz-euclide- https://tex.stackexchange.com/a/666573/197451 — js bibra, Mar 06 '24 at 04:37
Highlight the code and hit ctrl-k or click the code button at the top of the dialogue. Or put three back ticks on a line of their own before and after the code. — cfr, Mar 06 '24 at 18:32
Because you've asked two questions, you now have no good basis for accepting any answer, since each answer addresses one question. Please don't do this. Ask a followup question instead. We also can't sensibly link this to previous questions because we can't link to two. — cfr, Mar 06 '24 at 18:35
@cfr I thought asking a related question immediately was inappropriate. Sorry for causing the trouble. — Ypbor, Mar 07 '24 at 02:34
@Ypbor No problem. Asking a followup is fine. If you want to ask twenty, you should probably pace yourself, but two won't swamp the front page ;). Just link the first if they're related. — cfr, Mar 07 '24 at 04:40

score 3 · Answer 1 · answered Mar 06 '24 at 04:05

3

Use the calc library.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
\drawhelp linesnode{O} grid (7,6);
\node at (3,1)(a){A};
\node at (2,3)(b){B};
\node at ($1.2(a)+1.5(b)$){C};
\end{tikzpicture}
\end{document}

answered Mar 06 '24 at 04:05

Sandy G

42,558

Thanks! I just updated my post and added another question. – Ypbor Mar 06 '24 at 04:06

score 2 · Answer 2 · answered Mar 06 '24 at 04:44

for the intersection part with tkz-euclide

MWE

\documentclass[11pt,a4paper]{article}
\usepackage{tkz-euclide}
\usepackage{color}
\begin{document}
    \begin{tikzpicture}
        \tkzDefPoint(0,0){A} 
        \tkzDefPoint(6,5){B} 
        \tkzDrawSegmentblue
    \tkzDefPoint(0,5){C}
    \tkzDefPoint(6,0){D}
    \tkzDrawSegment[red](C,D)

    \tkzLabelPoints[xshift=-12pt, yshift=4pt](A,B,C,D)
    \tkzDrawPoints[size=4pt, fill=green, draw=green](A,B,C,D) 
    \tkzInterLL(A,B)(C,D) 

    \tkzGetPoint{O}

    \tkzDrawPoint[color=black,size=5mm,fill=white](O)

    \tkzLabelPoints[yshift=8mm](O)
\end{tikzpicture}

\end{document}

AndréC · Answer 3 · 2024-03-06T14:50:50.310

The intersection of two straight lines can be done in a simple way as was explained in the first versions of tikz, see manual 1.18 here: tikz manual version 1.18 Although undocumented in later versions of tikz, this syntax is still valid and very convenient for geometric constructions.

\coordinate[label=I] (I) at (intersection of A--B and C--D);

For the affine combination, there are barycentric coordinates, see the latest manual.

\coordinate[label=E](E) at (barycentric cs:A=1.2,B=0.2);

\documentclass[notitlepage, 12pt]{amsart}
\usepackage{amsthm, amsmath, amsaddr, amssymb, graphicx, dsfont,}
\usepackage[dvipsnames]{xcolor}
\renewcommand{\baselinestretch}{1.2}
\usepackage{tikz}
\usetikzlibrary{calc,intersections,through,backgrounds}
\usepackage{pgfplots} 
\usepackage[capposition=bottom]{floatrow}
\usepackage{float}
\pgfplotsset{compat=1.18}
\begin{document}
\thispagestyle{empty}
\begin{figure}[H]
\centering
\begin{tikzpicture}[xscale=18,yscale=18]
\coordinate[label=A] (A) at (0.2,0.3);
\coordinate[label=B] (B) at (0.3,0.2);
\coordinate[label=C] (C) at (0.4,0.2);
\coordinate[label=D] (D) at (0.4,0.5);
% affine combination of $A$ and $B$ 
\coordinatelabel=E at (barycentric cs:A=1.2,B=0.2);
% intersection of (AB) and (CD)
\coordinate[label=above right:I] (I) at (intersection of A--B and C--D);
\pgfgetlastxy{\XCoord}{\YCoord}
% construction of (AB) and (CD)
\draw($(A)!2.5!(B)$)--($(B)!1.5!(A)$);
\draw($(C)!1.5!(D)$)--($(D)!1.5!(C)$);
\foreach \a in {A,B,C,D,E,I}\draw[fill=black] (\a) circle(0.1pt);
\node[anchor=north,align=left] at (current bounding box.south){$x_I=\XCoord$\ $y_I= \YCoord$};
\end{tikzpicture}
\caption{}
\end{figure}
\end{document}

Thank you very much. My test suggests that even the line segment AB and line segment CD do not intersect directly (they have to be extended), the code still works. But how can I get the coordinate of the intersection point? (I mean get the numbers) — Ypbor, Mar 06 '24 at 06:31
Write this just after the intersection \pgfgetlastxy{\XCoord}{\YCoord} See Extract x, y coordinate of an arbitrary point in TikZ — AndréC, Mar 06 '24 at 14:14

How to extend a line with a specific proportion?

3 Answers3