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和数形结合思想解题 PowerPoint PPT Presentation


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活用反比例函数的性质. 和数形结合思想解题. 问题提出:九年级上册的数学课本中明确指出初中生会利用反比例函数的性质和图像解决某些实际问题。反比例函数的解析式和反比例函数的图像关于直角坐标系的原点成中心对称,为利用数和形的相互关系来解决数学问题创造了条件。把问题的数量关系转化为图形的性质,或者把图形的性质转化为数量关系,从而使复杂的问题简单化,抽象 的问题具体化 。. 问题提出: 九年级上册的数学课本中明确指出初中生会

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和数形结合思想解题

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4561755


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k


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1 y=kx(k0)

Ax1,y1)B x 2 ,y2 )x1y2 - 3x2y1

AB


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kk

y=kx

AB

x2= - x1 , y2= - y1;

x1y2- 3x2y1

=x1(-y1)-3(- x1y1)

=2x1y1= -10.


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2 y=kx(k0)

P,CPPB yB,BOC

y

B

P

o

x

C

P(x,y),C(- x , - y), B(0,y)

y=kx(k 0)


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3 A,C

AB,CDxBD,ABCD

A,C A(x,y),C(-x, -y),

B(x,0),D(-x,0).

ABD=

BCD

ABCD


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Y=k1x

A

Y=k2x

B

4 y=k1xy=k2x(k1k2)

AB

A(x1, B(x2, )

:


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5

AB

A4.

PQP

A,B,P,Q24P

P

A

O

B

Q


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P

A

O

B

E

F

Q

A(4,2)K=8P(x,y),xy=8

OPAQBPAO6,PAFO10

PAFE10.

xy=8,x,y


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y

B

P

o

x

C

P

A

O

B

E

F

Q


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6

6

- 6

-6

6

.()

x


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Y=-x+3,


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7

A. 3 B.2 C.1 D.0


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8 OABC

DOABC


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F

E

OABC

=OA OC

=2DF 2DE

=4DFDE

=4 2

=8


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9

OABCABFBCEOEBF2k.

OB OABC,FAB,k


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10 x>0)

1234.xy


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=


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