Question

已知一个直角三角形纸片,∠AOB=90°,OA=2,OB=4如图,将该纸片放置在平面直角坐标系中,折叠该纸P片求c坐

Answer 1

(1) A(2,0),B(0,4),AB:y=4-2x

(2) D(1,2),CD:y=(x+3)/2

C(0,3/2)

(3) ①M(1.5,1),N(0.5,3),PM+PN=(1.5-0.5)+(3-1)=3

②设P(0,y),PE=根号(1+y^2),PF=根号(1+(2-y)^2),

PE+PF的最小值＝2根号2 ,P(0,1)

(PE+PF)^2=(1+y^2)+(1+(2-y)^2)+2根号[(1+y^2)(1+(2-y)^2)]

=2(y-1)+4+2根号[(1+y^2)(1+(2-y)^2)]

4+2根号[(1+y^2)(1+(2-y)^2)]>0,只有当y=1时 (PE+PF)^2最小