This is a quadratic function synthesis problem involving many knowledge points. The coordinate characteristics of the points on the coordinate axis, the resolution function of the undetermined coefficient method to the straight line, the Pythagorean theorem, the nature of rotation and the classification idea are all involved, which is quite difficult. Look at the answer/exercise/math /800879. There are too many answers. Find it yourself. If you don't understand, ask me. I hope you can adopt them.

Parabola y = (- 1/4) x 2+(3/2) x-2 intersects with X axis at points A and B (point A is on the left of point B), intersects with Y axis at point C, and passes through points B and C respectively to make parallel lines between Y axis and X axis. The two parallel lines intersect at point D and rotate around point C counterclockwise by △BDC.

(1) Find the resolution function of the straight line where point B and point C are located;

(3) Is there a point P on the 3)BC line, which makes the triangle formed by points P, A and B similar to △BOC? If it exists, find the coordinates of point P.