初中數(shù)學(xué)教材解八年級(jí)上冊(cè)第十三章軸對(duì)稱(chēng)八年級(jí)數(shù)學(xué)上冊(cè)第十三章軸對(duì)稱(chēng)1畫(huà)軸對(duì)稱(chēng)圖

畫(huà)軸對(duì)稱(chēng)圖形(第2課時(shí))學(xué)習(xí)目標(biāo):1.在平面直角坐標(biāo)系中,會(huì)畫(huà)出關(guān)于x軸、y軸對(duì)稱(chēng)的點(diǎn),進(jìn)而探求關(guān)于x軸、y軸對(duì)稱(chēng)點(diǎn)的坐標(biāo)規(guī)律.2.通過(guò)找關(guān)于坐標(biāo)軸對(duì)稱(chēng)的點(diǎn)之間的規(guī)律,以及在驗(yàn)證規(guī)律正確的過(guò)程中,培養(yǎng)語(yǔ)言能力、觀察能力、歸納能力,養(yǎng)成良好的科學(xué)研究方法.3.在找點(diǎn)與繪圖的過(guò)程中,發(fā)展數(shù)形結(jié)合的思維意識(shí),形成數(shù)形結(jié)合的思想.學(xué)習(xí)過(guò)程:一、自主學(xué)習(xí)已知對(duì)稱(chēng)軸l和一個(gè)點(diǎn)A,你能作出點(diǎn)A關(guān)于l的對(duì)稱(chēng)點(diǎn)A'嗎?思考:這是一幅老北京城的示意圖,其中西直門(mén)和東直門(mén)是關(guān)于中軸線(xiàn)對(duì)稱(chēng)的.如果以天安門(mén)為原點(diǎn),分別以長(zhǎng)安街和中軸線(xiàn)為x軸和y軸建立平面直角坐標(biāo)系,根據(jù)如圖所示的東直門(mén)的坐標(biāo),你能說(shuō)出西直門(mén)的坐標(biāo)嗎?二、深化探究探究1:如圖,在平面直角坐標(biāo)系中你能畫(huà)出點(diǎn)A(2,-3)關(guān)于x軸的對(duì)稱(chēng)點(diǎn)嗎?點(diǎn)B(-1,2),C(-6,-5),D12,1，歸納:關(guān)于x軸對(duì)稱(chēng)的點(diǎn)的坐標(biāo)的特點(diǎn)是:______________.

練習(xí):1.點(diǎn)P(-5,6)與點(diǎn)Q關(guān)于x軸對(duì)稱(chēng),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(chēng),則a=,b=.

探究2:如圖,你能在平面直角坐標(biāo)系中畫(huà)出點(diǎn)A(2,-3)關(guān)于y軸的對(duì)稱(chēng)點(diǎn)嗎?點(diǎn)B(-1,2),C(-6,-5),D12,1歸納:關(guān)于y軸對(duì)稱(chēng)的點(diǎn)的坐標(biāo)的特點(diǎn)是:_________.

練習(xí):1.點(diǎn)P(-5,6)與點(diǎn)Q關(guān)于y軸對(duì)稱(chēng),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(chēng),則a=,b=.

小結(jié):點(diǎn)(x,y)關(guān)于x軸對(duì)稱(chēng)的點(diǎn)的坐標(biāo)為.

點(diǎn)(x,y)關(guān)于y軸對(duì)稱(chēng)的點(diǎn)的坐標(biāo)為.

三、深化提高1.完成下表.已知點(diǎn)A(3,-3)B(-1,2)C(8,-5)D(0,-1)E(4,0)關(guān)于x軸的對(duì)稱(chēng)點(diǎn)關(guān)于y軸的對(duì)稱(chēng)點(diǎn)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(chēng),則a=,b=.

若點(diǎn)P與點(diǎn)P'關(guān)于y軸對(duì)稱(chēng),則a=,b=.

3.【例1】已知△ABC的三個(gè)頂點(diǎn)的坐標(biāo)分別為(-3,5),B(-4,1),C(-1,3),作出△ABC關(guān)于y軸對(duì)稱(chēng)的圖形.【例2】四邊形ABCD的四個(gè)頂點(diǎn)的坐標(biāo)分別為A(-5,1),B(-2,1),C(-2,5),D(-5,4),分別作出四邊形關(guān)于y軸與x軸對(duì)稱(chēng)的圖形.解:點(diǎn)(x,y)關(guān)于y軸對(duì)稱(chēng)的點(diǎn)的坐標(biāo)為(-x,y),因此四邊形ABCD的頂點(diǎn)A,B,C,D關(guān)于y軸對(duì)稱(chēng)的點(diǎn)分別為A'(,),B'(,),C'(,),D'(,),依次連接A'B',B'C',C'D',D'A',就可得到與四邊形ABCD關(guān)于y軸對(duì)稱(chēng)的四邊形A'B'C'D'.類(lèi)似地,請(qǐng)你在圖上作出與四邊形ABCD關(guān)于x軸對(duì)稱(chēng)的圖形.

四、總結(jié)反思這節(jié)課你學(xué)到了什么?五、課堂檢測(cè)1.分別寫(xiě)出下列各點(diǎn)關(guān)于x軸和y軸對(duì)稱(chēng)的點(diǎn)的坐標(biāo).(-2,6)(1,-2)(-1,3)(-4,-2)(1,0)關(guān)于x軸對(duì)稱(chēng)的點(diǎn)關(guān)于y軸對(duì)稱(chēng)的點(diǎn)2.若點(diǎn)C(-2,-3)關(guān)于x軸的對(duì)稱(chēng)點(diǎn)為A,關(guān)于y軸的對(duì)稱(chēng)點(diǎn)為B,則△ABC的面積為.

3.已知點(diǎn)P(2m+1,m-3)關(guān)于y軸的對(duì)稱(chēng)點(diǎn)在第四象限,求m的取值范圍.4.如圖,利用關(guān)于坐標(biāo)軸對(duì)稱(chēng)的點(diǎn)的坐標(biāo)特點(diǎn),分別作出與△ABC關(guān)于x軸對(duì)稱(chēng)的△A'B'C'和關(guān)于y軸對(duì)稱(chēng)的△A″B″C″.參考答案一、自主學(xué)習(xí)過(guò)點(diǎn)A作直線(xiàn)l的垂線(xiàn)段(AO⊥l,垂足為O),延長(zhǎng)(AO到A')使得(A'O=AO),則A'就是點(diǎn)A關(guān)于直線(xiàn)l的對(duì)稱(chēng)點(diǎn).二、深化探究探究1:橫坐標(biāo)不變,縱坐標(biāo)互為相反數(shù)練習(xí):1.(-5,-6)5探究2:縱坐標(biāo)不變,橫坐標(biāo)互為相反數(shù)練習(xí):1.(5,6)-5三、深化提高1.已知點(diǎn)A(3,-3)B(-1,2)C(8,-5)D(0,-1)E(4,0)關(guān)于x軸的對(duì)稱(chēng)點(diǎn)(3,3)(-1,-2)(8,5)(0,1)(4,0)關(guān)于y軸的對(duì)稱(chēng)點(diǎn)(-3,-3)(1,2)(-8,-5)(0,-1)(-4,0)46-203.【例1】如圖所示.【例2】如圖所示.五、課堂檢測(cè)1.(-2,6)(1,-2)(-1,3)(-4,-2)(1,0)關(guān)于x軸對(duì)稱(chēng)的點(diǎn)(-2,-