28. As shown in the figure, in the equilateral triangle ABC, AB=4, point P is any point on AB, PE⊥BC is in E, EF⊥AC is in F, FQ⊥AB is in Q, let BP=X, AQ=Y, and fill in the blanks with the formula containing X.

(1) According to the meaning of the question, BE= BP,∴BE= X,∴EC=4- X, and ∵FC= EC.

∴ FC = _ _ _ _ _ _ ∴ AF = 4-FC = _ _ _ _ _ _ and aq = af, ∴ AQ = _ _ _ _ _ _ _ _

∴ The functional relationship between y and x is _ _ _ _ _ _ _ _ _ _ _ _,

(2) When AQ= 1.2, find the length of BP;

(3) When the length of BP is equal to what, point P and point Q coincide.

28 、( 1)2-0.25 x； 2+0.25 x； 1+0.25 x；

Y = 0.25x+ 1...4 points.

(2) When AQ= 1.2, y= 1.2.

1.2= 1+0. 125x

The solution is x= 1.6. When AQ= 1.2, BP = 1.6...6 points.

(3) When p and q coincide, BP+AQ=BQ+AQ=4.

That is, X+ 1+0. 125x=4, and the solution is x=

When BP=, point P and point Q coincide ... 8 points.

24.( 14 point) The linear function passes through the point (1 4), which intersects the X axis and the Y axis at point A and point B respectively. Point P (a, 0) moves on the positive semi-axis of X axis, and point Q (0, b) moves on the positive semi-axis of Y axis, PQ⊥AB.

(1), and draw the image of the linear function in rectangular coordinate system;

(2) Find the equivalence relation that A and B satisfy;

(3) If △APQ is an isosceles triangle, find △APQ.