132畫軸對(duì)稱圖形第2課時(shí)

1、13.2 畫軸對(duì)稱圖形第2課時(shí)1.1.探索利用坐標(biāo)來表示軸對(duì)稱探索利用坐標(biāo)來表示軸對(duì)稱. .2.2.掌握關(guān)于掌握關(guān)于x x軸、軸、y y軸對(duì)稱的點(diǎn)的坐標(biāo)特點(diǎn)軸對(duì)稱的點(diǎn)的坐標(biāo)特點(diǎn). .如如已知點(diǎn)已知點(diǎn)A A和一條直線和一條直線MNMN，你能畫出這個(gè)點(diǎn)關(guān)于已知直線，你能畫出這個(gè)點(diǎn)關(guān)于已知直線的對(duì)稱點(diǎn)嗎的對(duì)稱點(diǎn)嗎? ?A AAAM MN N A A就是點(diǎn)就是點(diǎn)A A關(guān)于直線關(guān)于直線MNMN的對(duì)稱點(diǎn)的對(duì)稱點(diǎn). .O O然后延長然后延長AOAO至至OA,OA,使使AO=OA.AO=OA.過點(diǎn)過點(diǎn)A A作作AOAOMNMN于于O,O,31425-2-4-1-3O12345-4-3-2-1A (2,3)A

2、(2,3)你能說出點(diǎn)你能說出點(diǎn)A A與點(diǎn)與點(diǎn)AA坐標(biāo)坐標(biāo)的關(guān)系嗎？的關(guān)系嗎？如圖，在平面直角坐標(biāo)如圖，在平面直角坐標(biāo)系中系中, ,你能畫出點(diǎn)你能畫出點(diǎn)A A關(guān)于關(guān)于x x軸的對(duì)稱點(diǎn)嗎軸的對(duì)稱點(diǎn)嗎? ?y yx x31425-2-4-1-312345-4-3-2-1A (2,3)A (2,3)A A(2,-3)(2,-3)點(diǎn)點(diǎn)A A與點(diǎn)與點(diǎn)AA橫坐標(biāo)相同，橫坐標(biāo)相同，縱坐標(biāo)互為相反數(shù)縱坐標(biāo)互為相反數(shù). .x xy yO31425-2-4-1-31 2 3 4 5-4 -3 -2 -1B (-4, 2)B (-4, 2)C(3, -4)C(3, -4)關(guān)于關(guān)于x x軸軸對(duì)稱的點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)具的坐

3、標(biāo)具有怎樣的有怎樣的關(guān)系？關(guān)系？在平面直角坐標(biāo)系中畫出下列各點(diǎn)在平面直角坐標(biāo)系中畫出下列各點(diǎn)關(guān)于關(guān)于x x軸的對(duì)稱點(diǎn)軸的對(duì)稱點(diǎn). .y yx xO31425-2-4-1-31 2 3 4 5-4 -3 -2 -1B (-4, 2)C(3, -4)B (-4, -2)C(3, 4)關(guān)于關(guān)于x x軸對(duì)稱的點(diǎn)的橫坐標(biāo)軸對(duì)稱的點(diǎn)的橫坐標(biāo)相同，縱坐標(biāo)互為相反數(shù)相同，縱坐標(biāo)互為相反數(shù). .y yx xO31425-2-4-1-312345-4-3-2-1A (2,3)A (-2,3)你能說出你能說出點(diǎn)點(diǎn)A A與點(diǎn)與點(diǎn)AA坐標(biāo)的坐標(biāo)的關(guān)系嗎？關(guān)系嗎？如圖，你能在平面直角坐如圖，你能在平面直角坐標(biāo)系中畫出點(diǎn)標(biāo)

4、系中畫出點(diǎn)A A關(guān)于關(guān)于y y軸的軸的對(duì)稱點(diǎn)嗎對(duì)稱點(diǎn)嗎? ?y yx xO31425-2-4-1-31 2 3 4 5-4 -3 -2 -1B (-4, 2)C(3, -4)B (4, 2)C(-3, -4)關(guān)于關(guān)于y y軸對(duì)軸對(duì)稱的點(diǎn)的稱的點(diǎn)的坐標(biāo)具有坐標(biāo)具有怎樣的關(guān)怎樣的關(guān)系？系？在平面直角坐標(biāo)系中畫出下列各點(diǎn)關(guān)于在平面直角坐標(biāo)系中畫出下列各點(diǎn)關(guān)于y y軸的對(duì)稱點(diǎn)軸的對(duì)稱點(diǎn). .y yx xO 關(guān)于關(guān)于y y軸對(duì)稱的點(diǎn)的橫坐標(biāo)互為相反數(shù)軸對(duì)稱的點(diǎn)的橫坐標(biāo)互為相反數(shù), , 縱坐標(biāo)縱坐標(biāo)相等相等. .點(diǎn)（點(diǎn)（x, yx, y）關(guān)于）關(guān)于x x軸對(duì)稱的點(diǎn)的坐標(biāo)為軸對(duì)稱的點(diǎn)的坐標(biāo)為_._.點(diǎn)（點(diǎn)（

5、x, yx, y）關(guān)于）關(guān)于y y軸對(duì)稱的點(diǎn)的坐標(biāo)為軸對(duì)稱的點(diǎn)的坐標(biāo)為_._.(x,(x,y)y)( (x,yx,y) )【解析解析】點(diǎn)點(diǎn)A(-3,5),A(-3,5),B(-4,1),C(-1,3)B(-4,1),C(-1,3)，關(guān)于，關(guān)于y y軸對(duì)稱點(diǎn)的坐標(biāo)分別為軸對(duì)稱點(diǎn)的坐標(biāo)分別為A(3,5),B(4,1),A(3,5),B(4,1),C(1,3).C(1,3).依次連接依次連接AB,BC,AB,BC,CA,CA,就得到就得到ABCABC關(guān)于關(guān)于y y軸對(duì)稱的圖形，軸對(duì)稱的圖形，即即ABC.ABC.A31425-2-4-1-3O O1 2 3 4 5-4 -3 -2 -1C BBAC已知

6、已知ABCABC的三個(gè)頂點(diǎn)的坐標(biāo)分別為的三個(gè)頂點(diǎn)的坐標(biāo)分別為A(-3A(-3，5),B(-45),B(-4，1),1),C(-1C(-1，3)3)，作出，作出ABCABC關(guān)于關(guān)于y y軸對(duì)稱的圖形軸對(duì)稱的圖形. .yx【例題例題】技巧技巧: :對(duì)于這類問題對(duì)于這類問題, ,只要先求出已知圖形中的一些特殊只要先求出已知圖形中的一些特殊點(diǎn)點(diǎn)( (如多邊形的頂點(diǎn)如多邊形的頂點(diǎn)) )的對(duì)應(yīng)點(diǎn)的坐標(biāo)的對(duì)應(yīng)點(diǎn)的坐標(biāo), ,描出并連接這些點(diǎn)描出并連接這些點(diǎn), ,就可以得到這個(gè)圖形的軸對(duì)稱圖形就可以得到這個(gè)圖形的軸對(duì)稱圖形. .1.1.點(diǎn)點(diǎn)P(-5, 6)P(-5, 6)與點(diǎn)與點(diǎn)Q Q關(guān)于關(guān)于x x軸對(duì)稱，則點(diǎn)

7、軸對(duì)稱，則點(diǎn)Q Q的坐標(biāo)為的坐標(biāo)為_._.2.2.點(diǎn)點(diǎn)M(aM(a, -5), -5)與點(diǎn)與點(diǎn)N(-2, b)N(-2, b)關(guān)于關(guān)于x x軸對(duì)稱，則軸對(duì)稱，則a=_,b =_.a=_,b =_.(- 5 ,-6 )(- 5 ,-6 )-2-25 5【跟蹤訓(xùn)練跟蹤訓(xùn)練】3.3.點(diǎn)點(diǎn)P(-3, 2)P(-3, 2)與點(diǎn)與點(diǎn)Q Q關(guān)于關(guān)于y y軸對(duì)稱，則點(diǎn)軸對(duì)稱，則點(diǎn)Q Q的坐標(biāo)為的坐標(biāo)為_._.4.4.點(diǎn)點(diǎn)M(aM(a, -6), -6)與點(diǎn)與點(diǎn)N(-2, b)N(-2, b)關(guān)于關(guān)于y y軸對(duì)稱，則軸對(duì)稱，則a=_, a=_, b =_. b =_.( 3 , 2 )( 3 , 2 )2 2-

8、6-61.1.完成下表完成下表: :已知點(diǎn)已知點(diǎn)(3,-3)(3,-3)(-1,2)(-1,2)(-8,(-8,- -5)5)(0,(0,- -1)1)(4,0)(4,0)關(guān)于關(guān)于x x軸的對(duì)稱點(diǎn)軸的對(duì)稱點(diǎn)關(guān)于關(guān)于y y軸的對(duì)稱點(diǎn)軸的對(duì)稱點(diǎn)(-3,-3)(-3,-3)(3, 3)(3, 3)(-1,-2)(-1,-2)(1, 2)(1, 2)(8,-5)(8,-5)(-8,5)(-8,5)(0, -1)(0, -1)(0,1)(0,1)(-4,0)(-4,0)（4 4，0 0）2.2.已知點(diǎn)已知點(diǎn)P(2a+b,-3a)P(2a+b,-3a)與點(diǎn)與點(diǎn)P(8,b+2).P(8,b+2).若點(diǎn)若點(diǎn)P

9、 P與點(diǎn)與點(diǎn)PP關(guān)于關(guān)于x x軸對(duì)稱，則軸對(duì)稱，則a=_,b=_.a=_,b=_.若點(diǎn)若點(diǎn)P P與點(diǎn)與點(diǎn)PP關(guān)于關(guān)于y y軸對(duì)稱，則軸對(duì)稱，則a=_,b=_.a=_,b=_.2 24 46 6-20-2031425-2-4-1-3012345-4-3-2-1x=1P(-2,3)M(-1,1)N (5,-2)N(-3,-2)M (3,1)P(4,3)3.3.如圖如圖, ,分別分別作出點(diǎn)作出點(diǎn)P,M,NP,M,N關(guān)于直線關(guān)于直線x=1x=1的對(duì)稱點(diǎn)的對(duì)稱點(diǎn), , 你能發(fā)現(xiàn)它你能發(fā)現(xiàn)它們坐標(biāo)之間們坐標(biāo)之間分別有什么分別有什么關(guān)系嗎關(guān)系嗎? ?y yx x（1 1）在平面直角坐標(biāo)系中）在平面直角坐標(biāo)系

10、中, ,點(diǎn)點(diǎn)( (x,yx,y) )關(guān)于直線關(guān)于直線x=1x=1對(duì)稱點(diǎn)對(duì)稱點(diǎn)的坐標(biāo)是多少的坐標(biāo)是多少? ?（2 2）在平面直角坐標(biāo)系中）在平面直角坐標(biāo)系中, ,點(diǎn)點(diǎn)( (x,yx,y) )關(guān)于直線關(guān)于直線x=-1x=-1對(duì)稱點(diǎn)對(duì)稱點(diǎn)的坐標(biāo)是多少的坐標(biāo)是多少? ? （3 3）在平面直角坐標(biāo)系中）在平面直角坐標(biāo)系中, ,點(diǎn)點(diǎn)( (x,yx,y) )關(guān)于直線關(guān)于直線y=1y=1對(duì)稱點(diǎn)對(duì)稱點(diǎn)的坐標(biāo)是多少的坐標(biāo)是多少? ?（4 4）在平面直角坐標(biāo)系中）在平面直角坐標(biāo)系中, ,點(diǎn)點(diǎn)( (x,yx,y) )關(guān)于直線關(guān)于直線y=-1y=-1對(duì)稱點(diǎn)對(duì)稱點(diǎn)的坐標(biāo)是多少的坐標(biāo)是多少? ?(-x+2,y)(-x+2,y)(-x-2,y)(-x-2,y)(x,-y+2)(x,-y+2)(x,-y-2)(x,-y-2) 1. 1.關(guān)于關(guān)于x x軸對(duì)稱的點(diǎn)橫坐標(biāo)相等，縱坐標(biāo)互為相反數(shù)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)于關(guān)于y y軸對(duì)稱的點(diǎn)橫坐標(biāo)互為相反數(shù)，縱坐標(biāo)相等軸對(duì)稱的點(diǎn)橫坐標(biāo)互為相反數(shù)，縱坐標(biāo)相等. . 2. 2.在平面直角坐標(biāo)系中畫一個(gè)圖形關(guān)于在平面直角坐標(biāo)系中畫一個(gè)圖形關(guān)于x x軸或軸或y y軸的對(duì)軸的對(duì)稱圖形：先求出已知圖形中的一些特殊點(diǎn)稱圖形：先求出已知圖形中的一些特殊點(diǎn)( (如多邊形的頂如多邊形的頂點(diǎn)點(diǎn)) )的對(duì)應(yīng)點(diǎn)的坐標(biāo)的對(duì)應(yīng)點(diǎn)的坐標(biāo), ,描出并連接這些點(diǎn)描出并連