(1) Find the coordinates of point A and point C;
(2) Fold △ABC in half, make point A coincide with point C, the crease passes through point AC and point B', and point AB and point D, and connect the CD, and find the analytical formula of the straight line where the CD is located (Figure 2);
(3) Is there a point P (except point B) in the coordinate plane, which makes the triangle with vertices A, P and C congruent with △ABC? If it exists, request all qualified P-point coordinates; If it does not exist, please explain why.
(1) When y=0, 0 =-2x+4? ∴A's coordinate is (2,0).
When x=0, y =-2x+4 = 4? The coordinate of ∴C is (0,4)
(2) let AD=x? ∴BD=4-x？ ∴CD？ =4+ 16+x？ -8 times
∵CD=AD？ ∴4+ 16+x？ -8x=x∴x=2.5
Let the resolution function of CD be y=kx+b? (k and b are constants, k≠0)
4=b from the meaning of the question? ∴k=-0.75
2.5=2k+bb=4
The resolution function is y =-0.75x+4.
(3) Existence, P1(0,0), P2 (16/5,8/5), P3 (-6/5, 12/5).
Make the P2⊥x axis, extend the intersection of CB and F, and let the coordinate of P2 be (x, y).
From the meaning of question (x-2)? +y？ =2?
(4-y)？ +x？ =4?
∴x=2y
Substitute y =-0.75x+4? y=-0.75×2y+4
∴ y = 8/5, x = 16/5 ∴ the coordinates of p2 are (16/5, 8/5).
Similarly, the coordinates of P3 are (-6/5, 12/5).