Solution: Point P can be a vertex of isosceles triangle AOP, and the coordinate of point P is (1, 2).
According to a characteristic of isosceles triangle, the vertical lines of the vertex and the bottom bisect the bottom vertically. According to this feature, the midpoint of line segment OA can be taken as the vertical line of X axis, and the intersection line y=-x+3 is at point P, and the coordinates of point P can be obtained by substituting y=-x+3 (1, 2).
2) Can point P be the vertex of right triangle AOP? If you can, find the coordinates of point P.
Solution: Point P can be a vertex of right triangle AOP.
When the angle AOP is a right angle, it is obvious that the coordinate of point P is (0,3).
When the angle OAP is a right angle, the vertical line with point A as the X axis intersects with point P. If x=2 is substituted into y=-x+3, the coordinate of point P is (2, 1).
3) Can point P be the vertex of isosceles right triangle AOP? If yes, find the coordinates of point P.
Point p can't be the vertex of isosceles right triangle AOP, 2) It shows that right triangle can't be isosceles triangle.
I hope it can be adopted and give some points (I hope no one plagiarized before answering)