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1、八年級數(shù)學(xué)組,平面直角坐標(biāo)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(diǎn),A,與點(diǎn),A,坐標(biāo)的關(guān)系嗎?,如圖,在平面直角坐標(biāo)系中,你能畫出點(diǎn),A,關(guān)于,x,軸的對稱點(diǎn)嗎,?,y,x,點(diǎn),A,與點(diǎn),A,橫坐標(biāo)相同,,縱坐標(biāo)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(guān)于,x,軸對稱的點(diǎn)的坐標(biāo)具有怎樣的關(guān)系?,在平面直角坐標(biāo)系中畫出下列各點(diǎn)關(guān)于,x,軸的對稱點(diǎn),.,y,x,
2、關(guān)于,x,軸對稱的點(diǎn)的橫坐標(biāo),相同,縱坐標(biāo)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(biāo)系中畫出點(diǎn),A,關(guān)于,y,軸的對稱點(diǎn)嗎,?,并觀察它們的關(guān)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(guān)于,y,軸對稱的點(diǎn)的坐標(biāo)具有怎樣的關(guān)系?,在平面直角坐標(biāo)系中畫出下列各點(diǎn)關(guān)于,y,軸的對稱點(diǎn),.,y,x,關(guān)于,y,軸對稱的點(diǎn)的橫坐標(biāo)互為相反數(shù),縱坐標(biāo)相等,.,點(diǎn)(
3、,x,y,)關(guān)于,x,軸對稱的點(diǎn)的坐標(biāo)為,_.,點(diǎn)(,x,y,)關(guān)于,y,軸對稱的點(diǎn)的坐標(biāo)為,_.,(x,y),(,x,y),關(guān)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(diǎn),P(2a+b,-3a),與點(diǎn),P(8,b+2).,若點(diǎn),P,與點(diǎn),P,關(guān)于,x,軸對稱,則,a=_ b=_.,若點(diǎn),P,與點(diǎn),P,關(guān)于,y,軸對稱,則,a=_ b=_.,2,4,6,-20,例,1,已知線段,AB,的兩個(gè)端點(diǎn)的坐標(biāo)分別為,A(-4,,,1),,,B(-1,,,
4、4),,作出線段,AB,關(guān)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(diǎn),A(-4,,,1),,,B(-1,,,4),,關(guān)于,y,軸對稱點(diǎn)的坐標(biāo)分別為,A(4,,,1),,,B(1,,,4),連接,A,、,B,,就得到線段,AB,關(guān)于,y,軸對稱的線段,AB,例,2,已知,ABC,的三個(gè)頂點(diǎn)的坐標(biāo)分別為,A(-4,,,1),,,B(-1,,,2),,,C(-3,,,4),,分別作出,ABC,關(guān)于,y,軸和,x,軸對稱的圖形,3,1,4,2,-
5、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(diǎn),A,和一條直線,MN,,你能畫出這個(gè)點(diǎn)關(guān)于已知直線的對稱點(diǎn)嗎,?,A,A,M,N,A,就是點(diǎn),A,關(guān)于直線,MN,的對稱點(diǎn),.,O,然后延長,AO,至,OA,使,AO=OA.,過點(diǎn),A,作,AO,MN,于,O,如何畫線段,AB,關(guān)于,直線,l,的對稱線段,A,B,?,A,B,A,B,作法:,1,、過點(diǎn),A,作直線,l,的垂線,垂足為點(diǎn),O,,在垂線上截,OA=OA,,點(diǎn),A,就是點(diǎn),A,關(guān)于直線,l,的對稱點(diǎn);,2,、類似地,作出點(diǎn),B,關(guān)于直線,l,
6、的對稱點(diǎn),B,;,3,、連接,AB.,線段,AB,即為所求。,o,1,、過點(diǎn),A,作直線,l,的垂線,垂足為點(diǎn),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(guān)于直線,l,對稱的圖形。,B,A,C,分析:,ABC,可以由三個(gè)頂點(diǎn)的位置確定,只要能分別作出這三個(gè)頂點(diǎn)關(guān)于直線,l,的對稱點(diǎn),連接這些對稱點(diǎn),就能得到要作的圖形。,l,作法:,2,、類似地,分別作出點(diǎn),B,、,C,關(guān)于直線,l,的對稱點(diǎn),B,、,C,;,3,、連接,AB,、,BC,、,CA,。,ABC,即為所求。,A,B,C,O,點(diǎn),A,就是點(diǎn),A,關(guān)于直線,l,的對稱點(diǎn);,B,A,
7、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(yīng)點(diǎn)的線段的中點(diǎn),并且垂直與這條線段,經(jīng)過線段的中點(diǎn)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(gè)圖形關(guān)于某直線對稱,那么對稱軸是任何一對對應(yīng)點(diǎn)所連線段的垂直平分線,(,2,)成軸對稱的兩個(gè)圖形中,對應(yīng)點(diǎn)的連線被對稱軸垂直平分,練習(xí),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(diǎn),P,M,N,關(guān)于直線,x=1,的對稱點(diǎn),你能發(fā)現(xiàn)它們坐標(biāo)之間分別有什么關(guān)系嗎,?,y,x,