Passage: Let X(a,p) , Y(b,q) and Z(c,r) be the points such that a ,...

Given that $a$, $b$, and $c$ are in AP, we have $2b = a + c$.

It is also given that $b = c$. Substituting this into the first equation gives $2b = a + b$, which implies $a = b$.

Therefore, $a = b = c$.

The coordinates of the points become $X(a, p)$, $Y(a, q)$, and $Z(a, r)$.

Since the $x$-coordinates of all three points are equal, they lie on the vertical line $x = a$.

This line is parallel to the $y$-axis.

Answer: $y$-axis