Prove that set is in general position

Question

Let $A$ be not empty set of points in general position contained in affine space $H \subset K^n$ . Let $q \in H-A$(where - is set complement) Prove set $A \cup \{q\}$ is in general position iff $q \not \in af(A)$

I'd be grateful for helping me int this sinceI have problems to understand the general position of points

Answer 1

Set of points/vectors in $R^d$ is in general position iff every (d+1) points are not in any possible hyperplane of dimension d.

See explanation of Affine hull. Then the requirement is natural and easy because of Affine hull of $A$ is family of hyperplanes containing the set $A$.