Four points a (0,1) B (2,1) C (3,4) d (- 1,2) in the plane rectangular coordinate system. Can these four points be on the same circle? Why?

Four points a (0,1) B (2,1) C (3,4) d (- 1,2) in the plane rectangular coordinate system. Can these four points be on the same circle? Why?

Of course. Four points are symmetrical about (1, x). If x = 3 obtained from the equation of equal radius, then they all pass the circle with (1, 3) as the center and 5 as the radius under the root sign

In the plane rectangular coordinate system, a (0,2), B (3,0), C (3,4)
(1) Finding the area of triangle ABC
(2) If there is a point P (m, 1) in the second quadrant, the area of the quadrilateral abop is expressed by the formula containing M
(3) If the area of the quadrilateral abop is equal to the area of the triangle ABC, find the coordinates of P
(4) If two points a and B move in 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, then, during the movement of points a and B, does the size of ∠ Q change? If not, find the value; if not, explain the reason

Let me see·····
(1) Subtract the area of triangle from the area of right trapezoid to get 6;
（2）Sabo=3,Spoa=2*m÷2=m,∴Sabop=m+3
（3）S=6,m=3
(4) The size of Q remains the same: make QN ⊥ AB and Q the vertical line of the two axes. From the question, we can see that QN = the distance to the two axes, so we can get ∠ q = 90 / 2 = 45 ° from the equilateral and equal angle