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The last question of Suzhou mathematics entrance examination in 2006
First of all, the first question:

Knowing the movement time, we can know the length of AQ, and then we can determine the coordinate of Q AQ/AB = (X coordinate of Q-2) /(5-2), and the ordinate can also be determined in the same way.

The second question:

This is an equation problem. The coordinate of point P is determined and it is also a function of X, and then the length of AP and the length of QP are calculated (using the coordinate of the previous Q) to make them equal, so that this equation can be solved.

The third question:

The coordinates of q and p are known for the first two questions, and then the coordinates of g can be obtained by averaging. You can observe the vertical and horizontal relationship in the coordinates of G, for example, set the abscissa to T and the ordinate to Y, so that you can solve X, and then bring the solved X back to the equation of y=G, so that you can get the relationship between Y and T (note that T is the abscissa now). This is the functional relationship you need. Look what this is.