Can I pre-define the points in Shamir's Secret Sharing algorithm With Shamir's secret sharing is it possible to pre-define the points returned by the algorithm?

For simplicity if I have (k, n) where k=2, and n=4, and I have the points X,Y,Z, and Q. Can I create the coefficients so that X,Y,Z, and Q are the points returned from the algorithm.

If yes will it still be secure (or secure enough)?

Edit:

Change my example to k=2 instead of k=1 to keep the comments from degenerating into a discussion on the merits of only needing a single piece of knowledge to access the secret.
With Shamir's secret sharing for the case of $k$ out of $n$, you construct a random polynomial of degree $k-1$, because $l$ points uniquely identify a polynomial of degree $k-1$.

The usual way to construct said polynomial is to uniformly choose coefficients $a_1$ through $a_{k-1}$ and setting $a_0=s$.

There is an alternative to that, where you choose $k-1$ points uniformly at random. The $k$th point is then $(0,s)$, you can compute the polynomial defined by those points and then compute the remaining $n-(k-1)$ points.
There is absolutely no difference between the two approaches.

So in summary: No that is not possible. You can freely choose at most $k-1$ shares. And also for the security to hold, those must be chosen uniformly at random.