(2011? Wenzhou) As shown in the figure, in the plane rectangular coordinate system, O is the origin of the coordinates, the coordinates of point A are (-4, 0), and the coordinates of point B are (0, b

(2011? Wenzhou) As shown in the figure, in the plane rectangular coordinate system, O is the origin of the coordinates, the coordinates of point A are (-4, 0), and the coordinates of point B are (0, b) (b>

(1) ①Suppose the analytical formula of straight line AB is y=kx+3,

Put x=-4, y=0 into: -4k+3=0,

∴k=34,

The analytical formula of ∴ straight line is: y=34x+3,

②P′ (-1, m),

p>

The coordinates of ∴ point P are (1, m),

∵ point P is on the straight line AB,

∴m=34×1+3=154;

(2) ∵PP′∥AC,

△PP′D∽△ACD,

∴P′DDC=P′PCA, that is, 2aa+ 4=13,

∴a=45;

(3) The following is discussed in three situations.

①When point P is in the first quadrant,

1) If ∠AP′C=90°, P′A=P′C (as shown in Figure 1)

Through point P′, draw P′H⊥x axis at point H.

∴PP′=CH=AH=P′H=12AC.

∴2a=12 (a+4)

∴a=43

∵P′H=PC=12AC, △ACP∽△AOB

∴OBOA=PCAC=12, that is, b4=12,

∴b=2

2) If ∠P′AC=90°, (as shown in Figure 2 ), then the quadrilateral P′ACP is a rectangle, then PP′=AC.

If △P?CA is an isosceles right triangle, then: P′A=CA,

∴2a=a+4

∴a=4

∵P′A=PC=AC, △ACP∽△AOB

∴OBOA=PCAC=1, that is, b4=1

∴b=4

3) If ∠P′CA=90°,

then point P′ and P are both in the first quadrant, which is contradictory to the condition.

∴△P′CA cannot be an isosceles right triangle with C as the right vertex.

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

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

The values ??of all a and b that meet the conditions are: Liked and Disliked What is your evaluation of this answer? 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