Given a quadrilateral represented by $$(X_n, Y_n)\;$$ I would like to obtain a specific point $$\;(A, B)\;$$ in the same quadrilateral when it changes perspective knowing only the vertex $$\;(X'_j, Y'_j)\;$$ like is shown in the image bellow:

So given the point $$\;(A, B)\;$$ of the left quadrilateral I would like to know which would be the value of $$\;(A', B')\;$$ when the quadrilateral is transformed.

Known parameters:

• $$(X_1, Y_1), (X_2, Y_2), (X_3, Y_3), (X_4, Y_4)$$
• $$(X'_1, Y'_1), (X'_2, Y'_2), (X'_3, Y'_3), (X'_4, Y'_4)$$
• $$(A, B)$$

Unknown parameters:

• $$(A', B')$$

The final goal is to known the coordinates of a specific point marked in an image in a new image that has a different perspective.