數(shù)學(xué)：同步授課課件-12.2.2《用坐標(biāo)表示軸對(duì)稱》(人教實(shí)驗(yàn)版八年級(jí)上)

12.2.2用坐標(biāo)表示軸對(duì)稱第1頁(yè)動(dòng)動(dòng)手畫(huà)一畫(huà)已知點(diǎn)A和一條直線MN，你能畫(huà)出這個(gè)點(diǎn)關(guān)于已知直線對(duì)稱點(diǎn)嗎?AA’MN∴A’就是點(diǎn)A關(guān)于直線MN對(duì)稱點(diǎn)。O然后延長(zhǎng)AO至OA’,使AO=OA’.過(guò)點(diǎn)A作AO⊥MN于O，第2頁(yè)·31425-2-4-1-3012345-4-3-2-1A(2,3)·A’(2,-3)你能說(shuō)出點(diǎn)A與點(diǎn)A’坐標(biāo)關(guān)系嗎？自主探究1如圖，在平面直角坐標(biāo)系中,你能畫(huà)出點(diǎn)A關(guān)于x軸對(duì)稱點(diǎn)嗎?第3頁(yè)·31425-2-4-1-3012345-4-3-2-1A(2,3)·A’(2,-3)點(diǎn)A與點(diǎn)A’橫坐標(biāo)相同，縱坐標(biāo)互為相反數(shù)如圖，在平面直角坐標(biāo)系中你能畫(huà)出點(diǎn)A關(guān)于x軸對(duì)稱點(diǎn)嗎?有什么特點(diǎn)？第4頁(yè)31425-2-4-1-3012345-4-3-2-1B(-4,2)··C(3,-4)·B’(-4,-2)·C’(3,4)關(guān)于x軸對(duì)稱點(diǎn)坐標(biāo)含有怎樣關(guān)系？想一想在平面直角坐標(biāo)系中畫(huà)出以下各點(diǎn)關(guān)于x軸對(duì)稱點(diǎn).第5頁(yè)31425-2-4-1-3012345-4-3-2-1B(-4,2)··C(3,-4)·B’(-4,-2)·C’(3,4)想一想關(guān)于x軸對(duì)稱點(diǎn)橫坐標(biāo)相同，縱坐標(biāo)互為相反數(shù)第6頁(yè)關(guān)于x軸對(duì)稱點(diǎn)橫坐標(biāo)相同，縱坐標(biāo)互為相反數(shù)1、點(diǎn)P(-5,6)與點(diǎn)Q關(guān)于x軸對(duì)稱，則點(diǎn)Q坐標(biāo)為_(kāi)_________.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)-25利用規(guī)律填一填第7頁(yè)自主探究2·31425-2-4-1-3012345-4-3-2-1A(2,3)·A’(-2,3)你能說(shuō)出點(diǎn)A與點(diǎn)A’坐標(biāo)關(guān)系嗎？如圖，你能在平面直角坐標(biāo)系中畫(huà)出點(diǎn)A關(guān)于y軸對(duì)稱點(diǎn)嗎?第8頁(yè)31425-2-4-1-3012345-4-3-2-1B(-4,2)··C(3,-4)·B’(4,2)·C’(-3,-4)關(guān)于y軸對(duì)稱點(diǎn)坐標(biāo)含有怎樣關(guān)系？想一想在平面直角坐標(biāo)系中畫(huà)出以下各點(diǎn)關(guān)于y軸對(duì)稱點(diǎn).第9頁(yè)關(guān)于y軸對(duì)稱的點(diǎn)的規(guī)律橫坐標(biāo)互為相反數(shù),縱坐標(biāo)相等.填一填1、點(diǎn)P(-3,2)與點(diǎn)Q關(guān)于y軸對(duì)稱，則點(diǎn)Q坐標(biāo)為_(kāi)_________.2、點(diǎn)M(a,-6)與點(diǎn)N(-2,b)關(guān)于y軸對(duì)稱，則a=_____,b=_____.(3,2)2-6第10頁(yè)點(diǎn)（x,y）關(guān)于x軸對(duì)稱點(diǎn)坐標(biāo)為_(kāi)_______.點(diǎn)（x,y）關(guān)于y軸對(duì)稱點(diǎn)坐標(biāo)為_(kāi)_______.(x,－y)(－x,y)

動(dòng)動(dòng)腦，一定行P:44第11頁(yè)練一練1、完成下表.已知點(diǎn)(3,-3)(-1,2)(-8,-5)(0,-1)(4,0)關(guān)于x軸對(duì)稱點(diǎn)關(guān)于y軸對(duì)稱點(diǎn)(-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(duì)稱，則a=_____b=_______.若點(diǎn)p與點(diǎn)p’關(guān)于y軸對(duì)稱，則a=_____b=_______.246-20第12頁(yè)典例分析解：點(diǎn)A(-3,5),B(-4,1),C(-1,3)，關(guān)于y軸對(duì)稱點(diǎn)坐標(biāo)分別為A’(3,5),B’(4,1),C’(1,3).依次連接A’B’,B’C’,C’A’,就得到△ABC關(guān)于y軸對(duì)稱△A’B’C’.····A31425-2-4-1-3012345-4-3-2-1··CBB’A’C’已知△ABC三個(gè)頂點(diǎn)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)稱圖形。第13頁(yè)技巧:對(duì)于這類(lèi)問(wèn)題,只要先求出已知圖形中一些特殊點(diǎn)(如多邊形頂點(diǎn))對(duì)應(yīng)點(diǎn)坐標(biāo),描出并連接這些點(diǎn),就能夠得到這個(gè)圖形軸對(duì)稱圖形.第14頁(yè)31425-2-4-1-3012345-4-3-2-1x=1·····P(-2,3)M(-1,1)N’(5,-2)N(-3,-2)M’(3,1)P’(4,3)拓展提升如圖,分別作出點(diǎn)P,M,N關(guān)于直線x=1對(duì)稱點(diǎn),你能發(fā)覺(jué)它們坐標(biāo)之間分別有什么關(guān)系嗎?·第15頁(yè)1、在平面直角坐標(biāo)系中,點(diǎn)(x,y)關(guān)于直線x=1對(duì)稱點(diǎn)

坐標(biāo)是多少?

2、在平面直角坐標(biāo)系中,點(diǎn)(x,y)關(guān)于直線x=-1對(duì)稱點(diǎn)坐標(biāo)是多少?

3、在平面直角坐標(biāo)系中,點(diǎn)(x,y)關(guān)于直線y=1對(duì)稱點(diǎn)坐標(biāo)是多少?

4、在平面直角坐標(biāo)系中,點(diǎn)(x,y)關(guān)于直線y=-1對(duì)稱點(diǎn)坐標(biāo)是多少?(-x+2,y)(-x-2,y)(x,-y+2)(x,-y-2)第16頁(yè)關(guān)于x軸對(duì)稱點(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)系中怎樣畫(huà)一個(gè)圖形關(guān)于x軸或y軸對(duì)稱圖形。先求出已知圖