Erdős problem 1090

Let $k\geq 3$. Does there exist a finite set $A\subset \mathbb{R}^2$ such that, in any $2$-colouring of $A$, there exists a line which contains at least $k$ points from $A$, and all the points of $A$ on the line have the same colour?

Erdős [Er75f] says Graham and Selfridge proved the answer is yes when $k=3$. Hunter has observed that, for sufficiently large $n$, a generic projection of $[k]^n$ into $\mathbb{R}^2$ has this property, by the Hales-Jewett theorem.