直線的對(duì)稱問(wèn)題

直線的對(duì)稱問(wèn)題1精選ppt學(xué)習(xí)目標(biāo)預(yù)習(xí)點(diǎn)睛1、點(diǎn)關(guān)于點(diǎn)對(duì)稱2、直線關(guān)于點(diǎn)對(duì)稱3、點(diǎn)關(guān)于直線對(duì)稱4、直線關(guān)于直線對(duì)稱2精選ppt對(duì)稱問(wèn)題中心對(duì)稱問(wèn)題點(diǎn)關(guān)于點(diǎn)的對(duì)稱線關(guān)于點(diǎn)的對(duì)稱軸對(duì)稱問(wèn)題點(diǎn)關(guān)于線的對(duì)稱線關(guān)于線的對(duì)稱3精選ppt軸對(duì)稱中心對(duì)稱有一條對(duì)稱軸:直線有一個(gè)對(duì)稱中心:點(diǎn)定義沿軸翻轉(zhuǎn)180°繞中心旋轉(zhuǎn)180°翻轉(zhuǎn)后重合旋轉(zhuǎn)后重合性質(zhì)1、兩個(gè)圖形是全等形2、對(duì)稱軸是對(duì)應(yīng)點(diǎn)連線的垂直平分線3、對(duì)稱線段或延長(zhǎng)線相交，交點(diǎn)在對(duì)稱軸上1、兩個(gè)圖形是全等形2、對(duì)稱點(diǎn)連線都經(jīng)過(guò)對(duì)稱中心，并且被對(duì)稱中心平分。4精選ppt一、點(diǎn)關(guān)于點(diǎn)對(duì)稱例1.點(diǎn)A(5,8)，B(-4，1)，試求A點(diǎn)關(guān)于B點(diǎn)的對(duì)稱點(diǎn)C的坐標(biāo)。解題要點(diǎn)：中點(diǎn)公式的運(yùn)用ACBxyOC(-13，-6)-4=5+x21=8+y2解:設(shè)C(x,y)那么得x=-13y=-6∴···5精選ppt二、點(diǎn)關(guān)于直線對(duì)稱例2.點(diǎn)A的坐標(biāo)為(-4,4)，直線l的方程為3x+y-2=0,求點(diǎn)A關(guān)于直線l的對(duì)稱點(diǎn)A’的坐標(biāo)。解題要點(diǎn)：k?kAA’=-1

AA’中點(diǎn)在l上

A··A′yxO(x，y)(2，6)-3·y-4x-(-4)=-13·-4+x2+4+y2-2=0解：設(shè)A′（x,y)·〔l為對(duì)稱軸〕6精選ppt例3.求直線l1:3x-y-4=0關(guān)于點(diǎn)P(2,-1)對(duì)稱的直線l2的方程。三、直線關(guān)于點(diǎn)對(duì)稱解題要點(diǎn)：

法一：l2上的任意一點(diǎn)的對(duì)稱點(diǎn)在l1上;

法二：L1∥L2點(diǎn)斜式或?qū)ΨQ兩點(diǎn)式法三：l1//l2且P到兩直線等距。解：設(shè)A(x，y)為l2上任意一點(diǎn)那么A關(guān)于P的對(duì)稱點(diǎn)A′在l1上∴3(4-x)-(-2-y)-4=0即直線l2的方程為3x-y-10=0·Al2l1yxOPA′··7精選ppt四、直線關(guān)于直線對(duì)稱例4.試求直線l1:x-y+2=0關(guān)于直線l2:x-y+1=0

對(duì)稱的直線l的方程。l2l1l解：設(shè)l方程為x-y+m=0則與距離等于與

距離l1l2l2l建立等量關(guān)系，解方程求mxoy8精選ppt.A.B9精選ppt.P.P’10精選ppt解題要點(diǎn)：(先判斷兩直線位置關(guān)系)（1）若兩直線相交，先求交點(diǎn)P,再在上取一點(diǎn)Q求其對(duì)稱點(diǎn)得另一點(diǎn)Q’兩點(diǎn)式求L方程L1求關(guān)于的對(duì)稱直線L的方程的方法L1L2則與距離等于與距離L1L2L2L建立等量關(guān)系，解方程求m(2)若‖

，設(shè)L方程為x-y+m=0L1L211精選ppt〔一〕常見(jiàn)的對(duì)稱點(diǎn)結(jié)論1.點(diǎn)關(guān)于原點(diǎn)的對(duì)稱點(diǎn)為;2.點(diǎn)關(guān)于點(diǎn)的對(duì)稱點(diǎn)為;3.點(diǎn)關(guān)于x軸的對(duì)稱點(diǎn)為;4.點(diǎn)關(guān)于y軸的對(duì)稱點(diǎn)為;5.點(diǎn)關(guān)于y=x的對(duì)稱點(diǎn)為;6.點(diǎn)關(guān)于y=-x的對(duì)稱點(diǎn)為;(-a,-b)(2m-a,2n-b)(a,-b)(b,a)(-b,-a)(-a,b)三、規(guī)律方法：12精選ppt1.直線關(guān)于原點(diǎn)的對(duì)稱直線的方程為:2.直線關(guān)于x軸的對(duì)稱直線的方程為:3.直線關(guān)于y軸的對(duì)稱直線的方程為:4.直線關(guān)于直線y=x的對(duì)稱直線的方程為:5.直線關(guān)于直線y=-x的對(duì)稱直線的方程為〔二〕常用的對(duì)稱直線結(jié)論:13精選ppt14精選p