In order to know three points a (1,2), B (4,1), C (3,4), take a point P on the line AB so that the line PQ passing through P and parallel to BC divides the triangle ABC into two parts: the triangle Apq and the quadrilateral pqcb, and their area ratio is s Triangle APQ:S Quadrilateral pqcb = 4:5, find the coordinates of point P There is no picture for this problem. I have to draw it myself. But I don't know how to do it. I want to get the process.

In order to know three points a (1,2), B (4,1), C (3,4), take a point P on the line AB so that the line PQ passing through P and parallel to BC divides the triangle ABC into two parts: the triangle Apq and the quadrilateral pqcb, and their area ratio is s Triangle APQ:S Quadrilateral pqcb = 4:5, find the coordinates of point P There is no picture for this problem. I have to draw it myself. But I don't know how to do it. I want to get the process.

Because PQ is parallel to BC and s triangle APQ:S Quadrilateral pqcb = 4:5, so s triangle APQ:ABC So AP: AB is equal to 2:3, so p is the trisection point of AB (AP is greater than BC). Using the formula, we can find that the point P is (5 / 3,8 / 3)
I think that's the answer,