如图,在平面直角坐标系xOy中,一次函数y=x+1与x,y轴分别交于点A,B,在直线AB上截取BB
1=AB,过点B
1分别作x,y轴的垂线,垂足分别为A
1 , C
1 , 得到矩形OA
1B
1C
1;在直线AB上截取
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmsub%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmsub%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%2C%3C%2Fmo%3E%3C%2Fmath%3E)
, 过点B
2分别作x,y轴的垂线,垂足分别为A
2 , C
2 , 得到矩形OA
2B
2C
2;在直线AB上截取
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmsub%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmsub%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmsub%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsub%3E%3Cmo%3E%2C%3C%2Fmo%3E%3C%2Fmath%3E)
, 过点B
3分别作x,y轴的垂线,垂足分别为A
3 , C
3 , 得到矩形OA
3B
3C
3;…,则点B
1的坐标是
;第3个矩形OA
3B
3C
3的面积是
;第n个矩形OA,BₙCₙ的面积是
.(用含n的式子表示,n是正整数)
![](http://tikupic.21cnjy.com/2025/01/09/c0/2e/c02eef421699b951555906a39d846425_101x106.jpeg)