In the plane rectangular coordinate system, if a (2,4), B (2, - 2), C (6, - 2) are known, then the coordinates of the center of the circle passing through a, B, C are______ ．

In the plane rectangular coordinate system, if a (2,4), B (2, - 2), C (6, - 2) are known, then the coordinates of the center of the circle passing through a, B, C are______ ．

It is known that the vertical bisector of a (2,4), B (2, - 2), C (6, - 2), AB is y = 1, the vertical bisector of BC is x = 4, and the center coordinates of the circle passing through a, B and C are (4,1). So the answer to this question is: (4,1)

As shown in the figure, in the plane rectangular coordinate system, three points a (0, a), B (B, 0), C (B, c) are known, where a, B, C satisfy the relation | A-2 | + (B-3) 2 = 0, C = 2b-a;
(1) Find the value of a, B, C;
(2) If there is a point P (m, 1) in the second quadrant, please use the formula containing m to represent the area of the quadrilateral abop. If the area of the quadrilateral abop is equal to the area of △ ABC, request the coordinates of point P;
(3) If B and a move on the positive half axis of X axis and Y axis respectively, let the bisector of the adjacent complementary angle of ∠ Bao and the bisector of the adjacent complementary angle of ∠ ABO intersect at a point Q in the first quadrant, will the size of ∠ Q change during the movement of points a and B? If it does not change, ask for its value. If it changes, please explain the reason

(1) From | A-2 | + (B-3) & # 178; = 0: a = 2, B = 3
C = 4 from C = 2b-a
(2) From the known M

Three points a (0,3) B (- 2,4) in the plane rectangular coordinate system are known
Finding the area of quadrilateral ABCO with three points a (0,3) B (- 2,4) C (- 3,0) in known plane rectangular coordinate system. 0 (0,0)

Draw the coordinates and mark the letters
Connect OB and calculate the area of triangle OAB and triangle OBC respectively
First, the area of triangle OAB = (2 * 3) / 2 = 3
OBC area of triangle = (3 * 4) / 2 = 6
So the quadrilateral area is 9