You're given the perspective image of an inverted pyramid shown above. $ABCD$ and $EFGH$ represent squares that lie in parallel planes. Point $N$ is the center of $ABCD$ and $M$ is the center of $EFGH$. Segment $NP$ is orthogonal to the plane of $ABCD$. You want to construct an identical pyramid whose base is centered at point $P$, and its apex is point $N$, and its base sides are parallel to the base sides of the original pyramid.
How can you construct the reflected pyramid ?
Details and Assumptions:
You have the $2D$ coordinates (in the image) of all the blue points $A$ through $H$. And that's all you have.
Let $A'B'C'D'$ be the reflected base. Diagonals $AC$, $EG$ and $A'C'$ meet at the same vanishing point, hence line $A'C'$ through $P$ can be constructed. And in the same way on can construct line $B'D'$.
If the plane of the image is parallel to the axis of the pyramid, then line $PN$ is parallel to $AA'$, $BB'$ etc. and that allows points $A'B'C'D'$ to be constructed.
If the plane of the image is not parallel to the axis of the pyramid then it is not possible to construct $A'B'C'D'$, unless a line parallel to $PN$ is given in the image. Failing that, we could choose at will a vanishing point $Q$ on the extension of $NP$ and draw $AA'$, $BB'$ etc. concurring to $Q$: the resulting quadrilateral $A'B'C'D'$ could be a possible base for the reflected pyramid.