對(duì)稱問(wèn)題甘淑清〔1〕點(diǎn)到直線距離公式：，〔2〕兩平行直線間的距離：，回顧：注意：用該公式時(shí)應(yīng)先將直線方程化為一般式；注意:運(yùn)用此公式時(shí)直線方程要化成一般式,并且X、Y項(xiàng)的系數(shù)要對(duì)應(yīng)相等.有關(guān)知識(shí)：1、直線互相垂直的條件：__________________2、P1(x1，y1)、P2(x2，y2)

的中點(diǎn)坐標(biāo)為_(kāi)_____________3、點(diǎn)(xo，yo)在直線Ax+By+C=0上的條件是__________________斜率存在，k1k2=－1Axo+Byo+C=0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。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)。知識(shí)運(yùn)用與解題研究一、點(diǎn)關(guān)于點(diǎn)對(duì)稱解題要點(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∴···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。二、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L(zhǎng)2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′··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。二、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。直線l2的方程為3x-y-10=0·L2L1YXOP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)。三、點(diǎn)關(guān)于直線對(duì)稱解題要點(diǎn)：k?kAA’=-1AA’中點(diǎn)在l上A··A′YXO-3·y-4x-(-4)=-13·-4+x2+4+y2-2=0(x，y)(2，6)解：設(shè)A′〔x,y)那么·〔L為對(duì)稱軸〕例4.試求直線l1:x-y-2=0關(guān)于直線l2:3x-y+3=0對(duì)稱的直線l的方程。

四、直線關(guān)于直線對(duì)稱L1L2Lx-y-2=03x-y+3=0P∴L：7x+y+6=0yXO解：P(，)-12-52得在上任取一點(diǎn)Q(2,0),求其關(guān)于的對(duì)稱點(diǎn)Q’(x,y)L1L2··Q(2,0),·Q’(x,y)3·y-0x-2=-13·y+02+3=0那么X+22求出Q’點(diǎn)坐標(biāo)后，兩點(diǎn)式求L方程。四、直線關(guān)于直線對(duì)稱··L1L2LPyXO·Q(2,0),Q’(x,y)解題要點(diǎn)：（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L1L2思考：假設(shè)l1//l2,如何求l1關(guān)于l2的對(duì)稱直線方程？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。四、直線關(guān)于直線對(duì)稱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mxoy四、直線關(guān)于直線對(duì)稱解題要點(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=0L1L2請(qǐng)大家完成下例填空題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;7.點(diǎn)關(guān)于x=m的對(duì)稱點(diǎn)為;8.點(diǎn)關(guān)于y=n的對(duì)稱點(diǎn)為;(-a,-b)(2m-a,2n-b)(a,-b)(b,a)(-b,-a)(2m-a,b)(-a,b)(a,2n-b)例題