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20 1 1 Wenzhou math test 24 answers
Solution: (1)① Let the analytical formula of straight line AB be y=kx+3,

Substituting x=-4 and y=0 gives: -4k+3=0,

∴k=3/4,

The analytical formula of the straight line is: y=3/4x+3,

② It is known that the coordinate of point P is (1, m),

∴m=3/4× 1+3= 15/4;

(2)∫PP '∨AC,

△PP'D∽△ACD,

∴P'D/DC=P'P/CA, that is, 2a/(a+4)= 1/3.

∴a=4/5;

(3) The following discussion is divided into three situations.

(1) When the point p is in the first quadrant,

1) If ∠ AP 'c = 90, P 'a = P 'c, (as shown in figure 1).

Passing point p' is the axis of P'H⊥x at point H.

∴PP'=CH=AH=P'H= 1/2AC,

∴2a=( 1/2)(a+4),

∴a=4/3,

∫P ' h = PC = 1/2AC,△ACP∽△AOB,

∴OB/OA=PC/AC= 1, that is, b/4= 1/2,

∴b=2.

2) If ∠ p 'ac = 90 and P'A=CA,

Then PP''=AC,

∴2a=a+4,

∴a=4,

∫P ' a = PC = AC,△ACP∽△AOB,

∴UB/OA=PC/AC= 1, that is, b/4= 1,

∴b=4.

3) If ∠ p 'ca = 90,

Then points p' and p are in the first quadrant, which contradicts the condition.

∴△P'CA can't be an isosceles right triangle with C as the right vertex.

② When point P is in the second quadrant, ∠P'CA is obtuse (as shown in Figure 3), at this time △P'CA cannot be an isosceles right triangle;

③ When p is in the third quadrant, ∠P'CA is an obtuse angle (as shown in Figure 4), at this time △P'CA cannot be an isosceles right triangle.

∴ All the values of A and B that meet the conditions are A = 4/3 and B = 2.

Or a = 4 and b = 4.