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1. As shown in the figure, in right-angle ABCD, DC=5cm, and there is a point E on DC. Fold the triangle AED along the straight line AE, so that the point D just falls on the side of BC. Let this point be f, and if the area of triangular ABF is 30cm2, what is the area of folded triangular AED? Square centimeter .. (with pictures)

Answer: Solution: The area of triangle ABF is 30cm2, and DC=AB=5cm.

∴BF= 12，

∴ in Rt△ABF, AF=52+ 122= 13.

∴BC=AD=AF= 13，

∴CF=BC-BF= 1，

∫EF = DE = 5-CE，

In Rt△EFC, (5-CE)2= 12+CE2.

∴CE=2.4，

∴DE=5-CE=5-2.4=2.6，

∴s△aed= 12× 13×2.6= 16.9cm2.

2. The lengths of two right-angled sides of a right-angled triangle are 4-2 and 4+2 respectively, so what is the area of this triangle? What's the circumference? .

Answer: ① The area of triangle =12× (4-2 )× (4+2) =12× (16-2) = 7;

② Assuming that the hypotenuse of a triangle is C, c2=(4-2)2+(4+2)2 can be obtained from Pythagorean theorem.

c2=36

That is, the hypotenuse c=6.

The perimeter of the triangle = 4-2+4+2+6 = 14.

3. The two intersections of inverse proportional function y=kx and linear function y=ax+b are A(- 1, -4) and B(2, m) respectively, so a+2b=? .

Answer: Substituting band A into the inverse proportional function results in k=4.

Substituting point b into the inverse proportional function results in m=2,

That is, point b is (2,2),

Substituting a and b into the linear function gives 2a+b=2( 1).

-a+b=-4(2)，

(1)+(2) =-2 A+2b.

So the answer is: -2.

4. Given that the inverse proportional function y=-4x and the linear function y=-x+3 intersect at point A and point B, what is the area of △AOB? .

Answer: If the inverse proportional function y=-4x is combined with the linear function y=-x+3, the coordinates of the intersection point are a (- 1, 4) and b (4, 1).

The coordinate of the intersection point C between the image with linear function y=-x+3 and the X axis is (3,0).

So △AOB area =△BOC area +△AOC area =12× 3×1+12× 3× 4 = 32+122 =152.

So the answer is: 152.

5. Point P( 1, a) is on the image of inverse proportional function y=kx, and its symmetry point about y axis is on the image of linear function y=2x+4. What is the analytical expression of this inverse proportional function? .

Answer: The symmetry point of point P (1, a) about the Y axis is (-1, a).

∵ point (-1, a) is on the image of linear function y=2x+4,

∴a=2×(- 1)+4=2，

∵ point p (1, 2) is on the image of inverse proportional function y=kx,

∴k=2，

The analytical formula of inverse proportional function is y = 2x.

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