I have the coordinates of three vertices of a triangle on a $2$-dimensional image plane - $(x_1,y_1), (x_2,y_2)$ and $(x_3,y_3)$. Their $3$-dimensional real world projection points are also known - $(x_1',y_1',z_1'), (x_2',y_2',z_2')$ and $(x_3',y_3',z_3')$ respectively. Now I have to find the $3$-dimensional projection of another arbitrary point $(x_c, y_c)$, how can I find them, if it is a linear projection?
Note: I do not have the information about $d$, where $d$ is distance between COP(center of projection) and PP(Projection plane/monitor). Then I assume that, I could use perspective projection equation.