集體備課平系中的軸對稱
八年級數(shù)學組,平面直角坐標系中的軸對稱,3,1,4,2,5,-2,-4,-1,-3,0,1,2,3,4,5,-4,-3,-2,-1,A(2,3),A(2,-3),你能說出點,A,與點,A,坐標的關系嗎?,如圖,在平面直角坐標系中,你能畫出點,A,關于,x,軸的對稱點嗎,?,y,x,點,A,與點,A,橫坐標相同,,縱坐標互為相反數(shù),.,3,1,4,2,5,-2,-4,-1,-3,0,1,2,3,4,5,-4,-3,-2,-1,B(-4,2),C(3,-4),B(-4,-2),C(3,4),關于,x,軸對稱的點的坐標具有怎樣的關系?,在平面直角坐標系中畫出下列各點關于,x,軸的對稱點,.,y,x,關于,x,軸對稱的點的橫坐標,相同,縱坐標互為相反數(shù),.,3,1,4,2,5,-2,-4,-1,-3,0,1,2,3,4,5,-4,-3,-2,-1,A(2,3),A,(-2,3),如圖,你能在平面直角坐標系中畫出點,A,關于,y,軸的對稱點嗎,?,并觀察它們的關系,y,x,3,1,4,2,5,-2,-4,-1,-3,0,1,2,3,4,5,-4,-3,-2,-1,B(-4,2),C(3,-4),B(4,2),C(-3,-4),關于,y,軸對稱的點的坐標具有怎樣的關系?,在平面直角坐標系中畫出下列各點關于,y,軸的對稱點,.,y,x,關于,y,軸對稱的點的橫坐標互為相反數(shù),縱坐標相等,.,點(,x,y,)關于,x,軸對稱的點的坐標為,_.,點(,x,y,)關于,y,軸對稱的點的坐標為,_.,(x,y),(,x,y),關于誰對稱,誰不變,1,、完成下表,:,(-3,-3),(3,3),(-1,-2),(1,2),(8,-5),(-8,5),(0,-1),(0,1),(-4,0),(,4,,,0,),2,、已知點,P(2a+b,-3a),與點,P(8,b+2).,若點,P,與點,P,關于,x,軸對稱,則,a=_ b=_.,若點,P,與點,P,關于,y,軸對稱,則,a=_ b=_.,2,4,6,-20,例,1,已知線段,AB,的兩個端點的坐標分別為,A(-4,,,1),,,B(-1,,,4),,作出線段,AB,關于,y,軸對稱的圖形,3,1,4,2,-2,-4,-1,-3,O,1,2,3,4,-4,-3,-2,-1,x,y,A(-4,,,1),B(-1,,,4),A,(4,,,1),B,(1,,,4),解:點,A(-4,,,1),,,B(-1,,,4),,關于,y,軸對稱點的坐標分別為,A(4,,,1),,,B(1,,,4),連接,A,、,B,,就得到線段,AB,關于,y,軸對稱的線段,AB,例,2,已知,ABC,的三個頂點的坐標分別為,A(-4,,,1),,,B(-1,,,2),,,C(-3,,,4),,分別作出,ABC,關于,y,軸和,x,軸對稱的圖形,3,1,4,2,-2,-4,-1,-3,O,1,2,3,4,-4,-3,-2,-1,x,y,-3,-5,5,5,-5,A,C,B,C,C,A,A,B,B,已知點,A,和一條直線,MN,,你能畫出這個點關于已知直線的對稱點嗎,?,A,A,M,N,A,就是點,A,關于直線,MN,的對稱點,.,O,然后延長,AO,至,OA,使,AO=OA.,過點,A,作,AO,MN,于,O,如何畫線段,AB,關于,直線,l,的對稱線段,A,B,?,A,B,A,B,作法:,1,、過點,A,作直線,l,的垂線,垂足為點,O,,在垂線上截,OA=OA,,點,A,就是點,A,關于直線,l,的對稱點;,2,、類似地,作出點,B,關于直線,l,的對稱點,B,;,3,、連接,AB.,線段,AB,即為所求。,o,1,、過點,A,作直線,l,的垂線,垂足為點,O,,,在垂線上截取,OA=OA,,,例,1,:如圖,已知,ABC,和直線,l,,作出與,ABC,關于直線,l,對稱的圖形。,B,A,C,分析:,ABC,可以由三個頂點的位置確定,只要能分別作出這三個頂點關于直線,l,的對稱點,連接這些對稱點,就能得到要作的圖形。,l,作法:,2,、類似地,分別作出點,B,、,C,關于直線,l,的對稱點,B,、,C,;,3,、連接,AB,、,BC,、,CA,。,ABC,即為所求。,A,B,C,O,點,A,就是點,A,關于直線,l,的對稱點;,B,A,C,l,A,B,C,O,觀察可知,OA=OA,,且,AA,垂直與,l,即對稱軸經(jīng)過連接對應點的線段的中點,并且垂直與這條線段,經(jīng)過線段的中點并且垂直于這條線段的直線叫做這條線段的垂直平分線,B,A,C,l,A,B,C,O,軸對稱的性質(zhì):,(,1,)如果兩個圖形關于某直線對稱,那么對稱軸是任何一對對應點所連線段的垂直平分線,(,2,)成軸對稱的兩個圖形中,對應點的連線被對稱軸垂直平分,練習,P122 T3,P124 T2,作業(yè),P126 T6,3,1,4,2,5,-2,-4,-1,-3,0,1,2,3,4,5,-4,-3,-2,-1,x=1,P(-2,3),M(-1,1),N(5,-2),N(-3,-2),M(3,1),P(4,3),提高 如圖,分別作出點,P,M,N,關于直線,x=1,的對稱點,你能發(fā)現(xiàn)它們坐標之間分別有什么關系嗎,?,y,x,