Find $y$-coordinate of point on three-dimensional rectangle.

Question

Given a quadrilateral in $3$-dimensional space and the coordinates of each of its vertices, can I find the $y$ of any point on this quadrilateral given this point's $x$ and $z$?

Answer 1

Use three of the four vertices to define the plane. This gives you the vector normal to the plane.

Then, choose any point on the quadrilateral (one of the vertices will do). Call this point $P$. Then solve for your point $Q = (x,y,z)$ such that the dot product of the normal vector and vector $PQ$ is zero.