Closed point and base change of scheme.

Closed point and base change of scheme.

Let $k$ be a field and $K/k$ be a field extension. For a scheme $X$ of
finite type over $k$, denote $X_K:=X\times_k \text{Spec}K$. Let $x\in X$
be a closed point and $x'\in X_K$ be a point lying over $x$. In this
situation, is $x'$ also a closed point? (This is true for $K/k$ is purely
inseparable extension since two schemes are homeomorphic.)