Draw the following points a (2,1), B (0,1), C (- 4, - 4), D (6, - 4) in the plane rectangular coordinate system, and connect them with line segments to form a quadrilateral ABCD (1) What special quadrilateral is ABCD? A:___ (2) Find a point P in the quadrilateral ABCD so that △ APB, △ BPC, △ CPD, △ APD are isosceles triangles, and request the coordinates of point P

Draw the following points a (2,1), B (0,1), C (- 4, - 4), D (6, - 4) in the plane rectangular coordinate system, and connect them with line segments to form a quadrilateral ABCD (1) What special quadrilateral is ABCD? A:___ (2) Find a point P in the quadrilateral ABCD so that △ APB, △ BPC, △ CPD, △ APD are isosceles triangles, and request the coordinates of point P

(1) As shown in the figure, it is easy to judge that the quadrilateral ABCD is an isosceles trapezoid. (2) from the meaning of the question, we know that point P must be on the vertical bisector of the two bottoms. Set point P (1, y), when point P is also on the vertical line of the two waists, PA = PC. from the distance formula between two points, we get 52 + (y + 4) 2 = 1 + (Y − 1) 2, and the solution is y = - 3.9

Place a right angle trapezoid AOCD, ad = 3, Ao = 8, OC = 5, P in the plane right angle coordinate system, so that the area of the two opposite groups of triangles are equal, and the point P sits

Let P (x, y) then
1/2 X3X(8 - y)=1/2 X5y ;
1/2 X8x＋1/2 X5y=1/2 X[1/2X(3+5)X8]
The solution is x = 17 / 8; y = 3
P coordinate is (17 / 8,3)