# Plotting a parallel line using tikz \draw plot

I'm trying to draw a line (PC2), that passes through some arbitrary point (A) and is parallel to another line (PC1).

PC1 is defined by a gradient (PCslp) and a y intercept (PCint). Obviously, as parallel lines, PC1 and PC2 have the same gradient. The y intercept is differnet, and can be calculated using point (A) and the gradient: take the y value of (A) and subtract the x value of (A) multiplied by the gradient (PCslp).

The code I am using is as follows:

\documentclass[tikz, border=2mm]{standalone}
\usepackage{tikz}
\usepackage{calc}

\usetikzlibrary{calc,intersections}

\begin{document}

\begin{tikzpicture}[
PC/.style={red, thick},
dot/.style={circle,fill=black,minimum size=4pt,inner sep=0pt,outer sep=-1pt}
]

% Define linear parameters
\def\PCint{0.2}   %Y-intercept
\def\PCslp{0.8}   %Slope
\def\PC{\x,{\PCslp*\x+\PCint}}

\draw[PC, domain=0:5]
plot (\PC)
node [right] {$PC_1$};

\draw [domain=0:5]
let
\p1=(61.28041pt, 26.23682pt),
\n1={\y1-\PCslp*\x1} in

% points the plot should pass through...
node [dot,label=above:{$A$}] at (\x1,\y1) {}
node [dot,label=above:{$B$}] at (0,\n1) {}

% first try for a plot...
plot ({\x,\PCslp*\x-\n1})
node [right] {$PC_2$};

\end{tikzpicture}
\end{document}

Unfortunately, the result I'm getting is not what I expected:

Can anybody point out what I'm doing wrong?

Cheers

nik

• First, plot ({\x,\PCslp*\x-\n1}) should be plot (\x,{\PCslp*\x+\n1}), but this doesn't work either. If you leave out the +\n1 you get the right slope, and if you leave out the \PCslp*x you get the right intercept. – John Kormylo May 7 '16 at 13:54
• Aha! \n1 is defined in screen units (-22.78769pt) and for some reason you cannot combine screen units and unscaled units in this calculation. – John Kormylo May 7 '16 at 14:03
• From the pgfmanual (page 132 of the current version): »An expression like (2+3cm,0) does not mean the same as (2cm+3cm,0). Instead, if <x> or <y> internally uses a mixture of dimensions and dimensionless values, then all dimensionless values are “upgraded” to dimensions by interpreting them as pt. So, 2+3cm is the same dimension as 2pt+3cm – esdd May 7 '16 at 14:17

A bit of a kludge, but it works:

\documentclass[tikz, border=2mm]{standalone}
\usepackage{tikz}
\usepackage{calc}

\usetikzlibrary{calc,intersections}

\begin{document}

\begin{tikzpicture}[
PC/.style={red, thick},
dot/.style={circle,fill=black,minimum size=4pt,inner sep=0pt,outer sep=-1pt}
]

% Define linear parameters
\def\PCint{0.2}   %Y-intercept
\def\PCslp{0.8}   %Slope
\def\PC{\x,{\PCslp*\x+\PCint}}

\draw[PC, domain=0:5]
plot (\PC)
node [right] {$PC_1$};

\draw [domain=0:5]
let
\p1=(61.28041pt, 26.23682pt),
\n1={\y1-\PCslp*\x1} in

% points the plot should pass through...
node [dot,label=above:{$A$}] at (\x1,\y1) {}
node [dot,label=above:{$B$}] at (0,\n1) {}

% first try for a plot...
plot[yshift=\n1] (\x,\PCslp*\x)
node [right,yshift=\n1] {$PC_2$};

\end{tikzpicture}
\end{document}