# TikZ: Intersection of two lines

what is the easiest way to determine the intersection of two lines? I tried

\usetikzlibrary{intersections}
\begin{tikzpicture}[every node/.style={black,above right}]
\draw[name path=line 1] (0,0) -- (2,2);
\draw[name path=line 2] (2,0) -- (0,2);
\fill[red,name intersections={of=line 1 and line 2}]
(intersection-1) circle (2pt) node {1}
(intersection-2) circle (2pt) node {2}
\end{tikzpicture}


• That doesn't look like it's the result of your code. And that code looks pretty easy to me, what would you like improved? – Loop Space Oct 12 '11 at 21:22
• Although, this question is quite old, let me ask you for some clarification: What do you understand under “line”? Your question and all answers only use two straight lines. For these you can use (intersection of c1--c2 and c3--c4). – Qrrbrbirlbel Jun 8 '13 at 4:00

The reason the code does not work as provided is that there is only one intersection, and so (intersection-2) does not exist. One way to alleviate this kind of issue is to specify total=\t to contain the total number of intersections and the use a foreach to loop through each intersection:

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

\begin{document}
\begin{tikzpicture}[every node/.style={black,above right}]
\draw[name path=line 1] (0,0) -- (2,2);
\draw[name path=line 2] (2,0) -- (0,2);
\fill[red,name intersections={of=line 1 and line 2,total=\t}]
\foreach \s in {1,...,\t}{(intersection-\s) circle (2pt) node {\footnotesize\s}};
\end{tikzpicture}
\end{document}


Reading the PGF Manual helps ;). See page 54ff, I made this from it:

\documentclass[parskip]{scrartcl}
\usepackage[margin=15mm]{geometry}
\usepackage{tikz}
\usetikzlibrary{calc,intersections,through,backgrounds}

\begin{document}

\begin{tikzpicture}
\coordinate (A) at (0,0);
\coordinate (B) at (3,3);
\draw [name path=A--B] (A) -- (B);
\coordinate (C) at (3,0);
\coordinate (D) at (0,1);
\draw [name path=C--D] (C) -- (D);
\path [name intersections={of=A--B and C--D,by=E}];
\node [fill=red,inner sep=1pt,label=-90:$E$] at (E) {};
\end{tikzpicture}

\end{document}


which results in:

An alternative, in the form of tkz-euclide.

\documentclass{article}
\usepackage{tkz-euclide}
\begin{document}
\begin{tikzpicture}
\tkzDefPoint(0,0){A}  \tkzDefPoint(2,2){B}
\tkzDefPoint(0,2){C}  \tkzDefPoint(2,0){D}
\tkzDrawSegments(A,B C,D)
\tkzInterLL(A,B)(C,D) \tkzGetPoint{E}
\tkzDrawPoints(E) \tkzLabelPoints[below](E)
\end{tikzpicture}
\end{document}


The first three lines define the points and draw the line segments between them. \tkzInterLL compute the intersection of the lines A--B and C--D, while \tkzGetPoint{E} gives the point a name. Finally the point is drawn and labeled.

You can mix this with "normal" TikZ code if you want to, e.g. (borrowing from Tom Bombadil):

\documentclass{article}
\usepackage{tkz-euclide}
\begin{document}
\begin{tikzpicture}
\coordinate (A) at (0,0);
\coordinate (B) at (3,3);
\coordinate (C) at (3,0);
\coordinate (D) at (0,1);
\draw (A) -- (B);
\draw (C) -- (D);
\tkzInterLL(A,B)(C,D) \tkzGetPoint{E}
\node [fill=red,inner sep=1pt,label=-90:$E$] at (E) {};
\end{tikzpicture}
\end{document}


This only uses tkz-euclide to find and name the intersection.

For the intersection of two segments, we don't need the intersections library. We can use directly in tikz points like (intersection of A--B and C--D).

\documentclass[tikz,border=5pt]{standalone}

\begin{document}
\begin{tikzpicture}
\draw (0,0) coordinate(A) -- (2,2) coordinate (B);
\draw (2,0) coordinate(C) -- (0,2) coordinate (D);
\node[red,scale=3] at (intersection of  A--B and C--D){.};
\end{tikzpicture}
\end{document}


Note: I don't think that this syntax is in the manual (of v3.0) ?

Edit: It looks like that this syntax is deprecated now :(

• this syntax is not described in tikz & pgf manual, v 3.0.1a. – Zarko Feb 13 '18 at 20:18
• @Zarko But it still works on version 3.0.1.a Which is very practical because it allows to solve a system of 2 equations to 2 unknown and thus to find the intersection of 2 straight lines whose intersection is not visible. – AndréC Apr 30 '18 at 14:24
• @AndréC, i didn'r say, that it not works :-), only that it is not described in recent official tikz version. – Zarko Apr 30 '18 at 14:45
• @Zarko Certainly, I had asked the team to add the documentation here sourceforge.net/p/pgf/feature-requests/108 – AndréC Apr 30 '18 at 14:51
• @AndréC, good news! now i hope that the new official tikz version will be realised soon :-)! – Zarko Apr 30 '18 at 15:00