12.2.2 用坐標(biāo)表示軸對(duì)稱

,12.2.2用坐標(biāo)表示軸對(duì)稱,動(dòng)動(dòng)手畫一畫,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(duì)稱點(diǎn)嗎?,A,A,M,N,A就是點(diǎn)A關(guān)于直線MN的對(duì)稱點(diǎn)。,O,然后延長(zhǎng)AO至OA,使OA=OA.,過點(diǎn)A作AOMN于O，,探究1：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(duì)稱點(diǎn)嗎?,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？,在平面直角坐標(biāo)系中畫出下列各點(diǎn)關(guān)于x軸的對(duì)稱點(diǎn).,B(-4,2),C(3,-4),B(-4,-2),C(3,4),思考：關(guān)于x軸對(duì)稱的點(diǎn)的坐標(biāo)具有怎樣的關(guān)系？,歸納：關(guān)于x軸對(duì)稱的點(diǎn)的坐標(biāo)的特點(diǎn)是：,橫坐標(biāo)相等,縱坐標(biāo)互為相反數(shù).,練習(xí):1、點(diǎn)P(-5,6)與點(diǎn)Q關(guān)于x軸對(duì)稱，則點(diǎn)Q的坐標(biāo)為_.2、點(diǎn)M(a,-5)與點(diǎn)N(-2,b)關(guān)于x軸對(duì)稱，則a=_,b=_.,(-5,-6),-2,5,探究2：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(duì)稱點(diǎn)嗎?,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？,在平面直角坐標(biāo)系中畫出下列各點(diǎn)關(guān)于y軸的對(duì)稱點(diǎn).,B(-4,2),C(3,-4),B(4,2),C(-3,-4),思考：關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)具有怎樣的關(guān)系？,歸納：關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)的特點(diǎn)是:,橫坐標(biāo)互為相反數(shù),縱坐標(biāo)相等.,練習(xí):1、點(diǎn)P(-5,6)與點(diǎn)Q關(guān)于y軸對(duì)稱，則點(diǎn)Q的坐標(biāo)為_.2、點(diǎn)M(a,-5)與點(diǎn)N(-2,b)關(guān)于y軸對(duì)稱，則a=_,b=_.,(5,6),2,-5,點(diǎn)（x,y）關(guān)于x軸對(duì)稱的點(diǎn)的坐標(biāo)為.點(diǎn)（x,y）關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)為.,小結(jié)：在平面直角坐標(biāo)系中，關(guān)于x軸對(duì)稱的點(diǎn)橫坐標(biāo)相等,縱坐標(biāo)互為相反數(shù).關(guān)于y軸對(duì)稱的點(diǎn)橫坐標(biāo)互為相反數(shù),縱坐標(biāo)相等.,(x,y),(x,y),1、完成下表.,(-2,-3),(2,3),(-1,-2),(1,2),(6,-5),(-6,5),(0,-1.6),(0,1.6),(-4,0),(4,0),練習(xí),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(duì)稱，則a=_b=_.若點(diǎn)P與點(diǎn)P關(guān)于y軸對(duì)稱，則a=_b=_.,2,4,6,-20,例已知ABC的三個(gè)頂點(diǎn)的坐標(biāo)分別為A(-3，5)，B(-4，1)，C(-1，3)，作出ABC關(guān)于y軸對(duì)稱的圖形。,解：點(diǎn)A(-3,5),B(-4,1),C(-1,3)，關(guān)于y軸對(duì)稱點(diǎn)的坐標(biāo)分別為A(3,5),B(4,1),C(1,3).依次連接AB,BC,CA,就得到ABC關(guān)于y軸對(duì)稱的ABC.,A,B,A,C,歸納:對(duì)于這類問題,只要先求出已知圖形中的一些特殊點(diǎn)(如多邊形的頂點(diǎn))的對(duì)應(yīng)點(diǎn)的坐標(biāo),描出并連接這些點(diǎn),就可以得到這個(gè)圖形的軸對(duì)稱圖形.,1、學(xué)習(xí)了在平面直角坐標(biāo)系中，關(guān)于x軸和y軸對(duì)稱的點(diǎn)的坐標(biāo)的特點(diǎn)。,這節(jié)課你學(xué)到了什么？,關(guān)于x軸對(duì)稱的點(diǎn)橫坐標(biāo)相等,縱坐標(biāo)互為相反數(shù).關(guān)于y軸對(duì)稱的點(diǎn)橫坐標(biāo)互為相反數(shù),縱坐標(biāo)相等.,2、學(xué)習(xí)了在平面直角坐標(biāo)系中如何畫一個(gè)圖形關(guān)于x軸或