Given that the side length of the square ABCD is 2, the point Q is the midpoint of the side BC, and the point P is outside the square and satisfies ∠APD=135∘, then PQ is the maximum
Q. Given that the side length of the square ABCD is 2, the point Q is the midpoint of the side BC, and the point P is outside the square and satisfies ∠APD=135∘, then PQ is the maximum
Calculate Points Coordinates: Calculate the coordinates of points B, C, and Q.Since ABCD is a square with side length 2, let A be at (0,0), B at (2,0), C at C0, and C1 at C2. The midpoint Q of C4 is then at C5.
Determine Point P Coordinates: Determine the coordinates of point P using the angle condition.Given ∠APD=135∘, we can use trigonometry to find P. However, without additional information about the distance from A or D to P, we cannot directly calculate P's coordinates.