How to navigate away from a given point in tikz?

Question

I know this is a very basic question but I somehow have not found an answer to this searching through the documentation (although I have to say it is probably my bad).

But how am I able to navigate from a given point in a tikz graphic? I am using tikz and tkz-euclide. And if I grab any point in space, how do I define another point to just be +1 in every direction away from that one? Like if I have my point A at (1/1) and I want A' to always be 1 away in x direction and two away in y direction, how do I do that?

If this helps:

\usepackage{tikz}
\usepackage{tkz-euclide}
\tkzDefPoint(1,1){A}

Answer 1

See Derived \coordinate in TikZ for various ways of defining relative coordinates with plain TikZ.

tkz-euclide has \tkzDefShiftPoint for this sort of thing, e.g. \tkzDefShiftPoint[B](1,2){A} to define B 1 unit lengths right and two units up relative to A.

\documentclass[border=4mm]{standalone}
\usepackage{tkz-euclide}

\usetikzlibrary{calc, positioning}
\begin{document}
\begin{tikzpicture}
\draw[help lines] (0,0) grid (4,4);

\tkzDefPoint(1,1){A}
\tkzDefShiftPoint[A](1,2){B}
%\path (A) ++(1,2) coordinate (B);
%\coordinate (B) at ([shift={(1,2)}]A);
%\coordinate [above right=2 and 1 of A] (B); % requires positioning library
%\coordinate (B) at ($(A)+(1,2)$); % requires calc library

\draw [->] (A) -- (B);
\end{tikzpicture}
\end{document}