Question

如图,过点B(4,2)分别作x轴,y轴垂线,垂足分别为点C,A.反比例函数y=k/x的图像经

Answer 1

(1)

A(0,2),B(4,2),M(2,2)

y = k/x,2 = k/2,k = 4

y = 4/x

取x = 4,y = 4/4 = 1,N(4,1)

C(4,0),B(4,2),BC的中点(4,1),N是BC的中点

(2)

四边形OMBN的面积 = 梯形ACBM的面积 - 三角形ACN的面积

= (1/2)(MB + OC)*CB - (1/2)*OC*CN

= (1/2)(2 + 4)*2 - (1/2)*4*1

= 4

(3)

B(u,v),M(u/2,v),N(u,v/2)

四边形OMBN的面积 = 梯形ACBM的面积 - 三角形ACN的面积

= (1/2)(MB + OC)*CB - (1/2)*OC*CN

= (1/2)(u/2 + u)*v - (1/2)u*(v/2)

= 3uv/4 - uv/4

= uv/2 = a

y = k/x

k = xy = (u/2)*v = uv/2 = a

y = a/x