In the plane rectangular coordinate system, the following points a (2,1) B (0,1) C (- 2,3), D (4,3) are described, and each point is connected by line segments to form a quadrilateral ABCD 1. What special figure is quadrilateral ABCD? 2. Find a point P in the plane of the quadrilateral ABCD so that △ APB, △ BPC, △ CPD, △ APD are isosceles triangles. Please write the coordinates of point P

In the plane rectangular coordinate system, the following points a (2,1) B (0,1) C (- 2,3), D (4,3) are described, and each point is connected by line segments to form a quadrilateral ABCD 1. What special figure is quadrilateral ABCD? 2. Find a point P in the plane of the quadrilateral ABCD so that △ APB, △ BPC, △ CPD, △ APD are isosceles triangles. Please write the coordinates of point P

1 trapezoid
Because the quadrilateral ABCD is a symmetrical figure, in order to make △ APB and △ cpd isosceles triangle, P should be on the vertical bisector of ab
If △ BPC and △ APD are isosceles triangle, P should also be on the vertical bisector of BC. Point P is the intersection of two lines
The vertical bisector of AB is x = 1. The vertical bisector of BC is y = x + 3
The coordinates of point P are (1,4)

Describe the following points a (0,4), B (- 4,0), C (6,0), D (2,4) in the plane rectangular coordinate system, and connect them with line segments to form a quadrilateral ABCD. (1) what is the special quadrilateral ABCD______ (2) In the plane rectangular coordinate system, if PA = Pb = PC = PD, then the coordinate of point P is______ (3) is there a point P in the quadrilateral ABCD such that △ APB, △ BPC, △ CPD, △ APD are isosceles triangles? If yes, ask for the coordinates of point p; if not, please explain the reason

(1) As shown in the figure, it is an isosceles trapezoid; (2) point P must be on the vertical bisector of the two bottoms. Set point P (1, y), and point P is also on the middle perpendicular of the two waists: (0 − 1) 2 + (Y − 4) 2 = (− 4 − 1) 2 + (0 − y) 2. The solution is: y = - 1, so p (1, - 1); (3) when point P is not on the middle perpendicular of the two waists, set point P (1

Point a (2,1) B (0,1), C (- 4, - 3), D (6, - 3) are described in the plane rectangular coordinate system, and the points are connected by line segments to form a quadrilateral ABCD
Then the perimeter of the quadrilateral ABCD is

It is obviously a trapezoid, AB is parallel to CD, ab = 2, CD = 10, height equals 4, and its area is (2 + 10) * 4 / 2 = 24

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

Junior high school mathematics solver
(1) As long as the drawing is standard and accurate, it is easy to judge that the quadrilateral ABCD is isosceles trapezoid;
(2) It is known from (1) that point P must be on the vertical bisector of the two bottoms. Let point P (1, y) be discussed in two cases: when point P is also on the vertical line of the two waists, PA = PC; when point P is not on the vertical line of the two waists, DB = DP, then the distance between two points can be calculated by the formula
(2) Point P must be on the vertical bisector of the two bottoms
Let P (1, y),
When the point P is also on the vertical line of the two waists, PA = PC, from the distance formula between the two points, 52 + (y + 4) 2 = 1 + (Y-1) 2,
The solution is y = - 3.9;
When the point P is not on the vertical line of the two waists, DB = DP, from the distance formula between the two points, 52 + (4 + y) 2 = 42 + 52,
The solution is y = 0;
The coordinates of point P are (1, - 3.9) and (1,0)