用坐標(biāo)表示軸對(duì)稱12

1、 12.2.2用坐標(biāo)表示軸對(duì)稱用坐標(biāo)表示軸對(duì)稱4(4,0)(0,0)探究1：如圖，在平面直角坐標(biāo)系中你能畫出點(diǎn)A關(guān)于x軸的對(duì)稱點(diǎn)嗎?31425-2-4-1-3012345-4-3-2-1A (2,3)A(2,-3)你能說出點(diǎn)A與點(diǎn)A坐標(biāo)的關(guān)系嗎？5x y 請(qǐng)同學(xué)們?cè)谧鴺?biāo)系中多找?guī)渍?qǐng)同學(xué)們?cè)谧鴺?biāo)系中多找?guī)讉€(gè)點(diǎn)個(gè)點(diǎn),并畫出它們關(guān)于軸對(duì)稱并畫出它們關(guān)于軸對(duì)稱的點(diǎn)的點(diǎn),然后觀察已知點(diǎn)與對(duì)稱然后觀察已知點(diǎn)與對(duì)稱點(diǎn)的橫坐標(biāo)和點(diǎn)的橫坐標(biāo)和縱坐標(biāo)縱坐標(biāo) 有什么有什么變化變化?在平面直角坐標(biāo)系中畫出下列各點(diǎn)關(guān)于x軸的對(duì)稱點(diǎn).31425-2-4-1-301 2 3 4 5-4 -3 -2 -1B (-4, 2)C

2、(3, -4)B (-4, -2)C(3, 4)思考：思考：關(guān)于關(guān)于x軸軸對(duì)稱的對(duì)稱的點(diǎn)的坐點(diǎn)的坐標(biāo)具有標(biāo)具有怎樣的怎樣的關(guān)系？關(guān)系？x y 通過探究你能用語言歸納關(guān)于通過探究你能用語言歸納關(guān)于 x 軸軸對(duì)稱的點(diǎn)坐標(biāo)規(guī)律嗎？對(duì)稱的點(diǎn)坐標(biāo)規(guī)律嗎？歸納：關(guān)于x軸對(duì)稱的點(diǎn)的坐標(biāo)的特點(diǎn)是:橫坐標(biāo)橫坐標(biāo)相等相等,縱坐標(biāo)縱坐標(biāo)互為相反數(shù)互為相反數(shù).練習(xí)練習(xí): :1 1、點(diǎn)、點(diǎn)P(-5, 6)P(-5, 6)與點(diǎn)與點(diǎn)QQ關(guān)于關(guān)于x x軸對(duì)稱，則點(diǎn)軸對(duì)稱，則點(diǎn)QQ的坐標(biāo)為的坐標(biāo)為_._.2 2、點(diǎn)、點(diǎn)M (a, -5)M (a, -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

3、a=_, a=_, b =_.b =_.(- 5 , -6 )(- 5 , -6 )-2-25 57探究2：如圖，你能在平面直角坐標(biāo)系中畫出點(diǎn)A關(guān)于y軸的對(duì)稱點(diǎn)AA嗎?31425-2-4-1-3012345-4-3-2-1A (2,3)A(-2,3)你能說出點(diǎn)A與點(diǎn)A坐標(biāo)的關(guān)系嗎？x y 在平面直角坐標(biāo)系中畫出下列各點(diǎn)關(guān)于y軸的對(duì)稱點(diǎn).31425-2-4-1-301 2 3 4 5-4 -3 -2 -1B (-4, 2)C(3, -4)B (4, 2)C(-3, -4)思考：思考：關(guān)于關(guān)于y軸軸對(duì)稱的對(duì)稱的點(diǎn)的坐點(diǎn)的坐標(biāo)具有標(biāo)具有怎樣的怎樣的關(guān)系？關(guān)系？x y 歸納：關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)的特

4、點(diǎn)是:橫坐標(biāo)橫坐標(biāo)互為相反數(shù)互為相反數(shù),縱坐標(biāo)縱坐標(biāo)相等相等.練習(xí)練習(xí): :1 1、點(diǎn)、點(diǎn)P(-5, 6)P(-5, 6)與點(diǎn)與點(diǎn)QQ關(guān)于關(guān)于y y軸對(duì)稱，則點(diǎn)軸對(duì)稱，則點(diǎn)QQ的坐標(biāo)為的坐標(biāo)為_._.2 2、點(diǎn)、點(diǎn)M (a, -5)M (a, -5)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 =_.( 5 , 6 )( 5 , 6 )2 2-5-5小結(jié)：在平面直角坐標(biāo)系中，關(guān)于小結(jié)：在平面直角坐標(biāo)系中，關(guān)于x軸對(duì)稱的點(diǎn)軸對(duì)稱的點(diǎn)橫坐標(biāo)相等橫坐標(biāo)相等,縱坐標(biāo)互為相反縱坐標(biāo)互為相反數(shù)數(shù).關(guān)于關(guān)于y軸對(duì)稱的點(diǎn)軸對(duì)稱的點(diǎn)橫坐標(biāo)互為相反數(shù)橫

5、坐標(biāo)互為相反數(shù),縱坐標(biāo)相等縱坐標(biāo)相等.點(diǎn)（點(diǎn)（a, b）關(guān)于關(guān)于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)（a, b）關(guān)于關(guān)于y軸對(duì)稱的點(diǎn)軸對(duì)稱的點(diǎn)的坐標(biāo)為的坐標(biāo)為_.(a, b)( a, b)已知點(diǎn)關(guān)于已知點(diǎn)關(guān)于x軸或軸或y軸對(duì)稱的點(diǎn)的坐標(biāo)變化規(guī)軸對(duì)稱的點(diǎn)的坐標(biāo)變化規(guī)律律:( P44)1、完成下表、完成下表.已知點(diǎn)(2,-3)(-1,2)(-6,-5)(0,-1.6) (4,0)關(guān)于x軸的對(duì)稱點(diǎn)關(guān)于y軸的對(duì)稱點(diǎn)(-2, -3)(2, 3)(-1,-2)(1, 2)(6, -5)(-6, 5)(0, -1.6)(0,1.6)(-4,0)(4,0)2、已知點(diǎn)、已知點(diǎn)P(2a+b,-3a)與

6、點(diǎn)與點(diǎn)P(8,b+2).若點(diǎn)若點(diǎn)p與點(diǎn)與點(diǎn)p關(guān)于關(guān)于x軸對(duì)稱，則軸對(duì)稱，則a=_ b=_.若點(diǎn)若點(diǎn)p與點(diǎn)與點(diǎn)p關(guān)于關(guān)于y軸對(duì)稱，則軸對(duì)稱，則a=_ b=_.練 習(xí)246-20(搶答搶答)例：已知ABC的三個(gè)頂點(diǎn)的坐標(biāo)分別為A(-3，5),B(- 4，1),C(-1，3)，作出ABC關(guān)于y軸對(duì)稱的圖形。解：點(diǎn)解：點(diǎn)A(-3,5),B(-4,1),A(-3,5),B(-4,1),C(-1,3)C(-1,3)，關(guān)于，關(guān)于y y軸對(duì)稱軸對(duì)稱點(diǎn)的坐標(biāo)分別為點(diǎn)的坐標(biāo)分別為A(3,5), A(3,5), B(4,1),C(1,3).B(4,1),C(1,3).依次連依次連接接AB,BC,CA,AB,BC,C

7、A,就得到就得到ABCABC關(guān)于關(guān)于y y軸對(duì)軸對(duì)稱的稱的ABC.ABC.A31425-2-4-1-301 2 3 4 5-4 -3 -2 -1cBBAC 歸納歸納: :先求出已知圖形中的先求出已知圖形中的 特殊點(diǎn)特殊點(diǎn)( (如多邊形的頂點(diǎn)或端點(diǎn)如多邊形的頂點(diǎn)或端點(diǎn)) )的對(duì)應(yīng)點(diǎn)的的對(duì)應(yīng)點(diǎn)的坐標(biāo)坐標(biāo), ,描出并連接這些點(diǎn)描出并連接這些點(diǎn), ,就可就可 得到這得到這個(gè)圖形的軸對(duì)稱圖形個(gè)圖形的軸對(duì)稱圖形. .x y 例 如圖，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),分別作出與四邊形ABCD關(guān)于y軸和關(guān)于x軸對(duì)稱的圖形。012345xy1

8、3425-2-1-5 -4-3-4-3-2-1ADCBADCBBDCA 練習(xí):P45 2 .3 (1,2)012345-4-3-2-131425-2-4-1-36y=-1A（-2，-3）B（-2，1）xy （拓展提高）思考：（P134探究3）:（拓展提高）如圖,分別作出點(diǎn)P,M,N關(guān)于直線x=1的對(duì)稱點(diǎn), 你能發(fā)現(xiàn)它們坐標(biāo)之間分別有什么關(guān)系嗎?31425-2 -1 012345-4-3-2-1x=1P(-24)M(-1,1)N(5,-2)N(-3,-2)M(3,1)P(4,4)x y , 結(jié)論：結(jié)論： 1 1、點(diǎn)（、點(diǎn)（x,yx,y) )關(guān)于直線關(guān)于直線x=mx=m對(duì)稱的點(diǎn)的坐標(biāo)為對(duì)稱的點(diǎn)的坐

9、標(biāo)為(2m-x,y),(2m-x,y),即若兩點(diǎn)即若兩點(diǎn)(x(x1 1,y,y1 1) )、（、（x x2 2,y,y2 2) )關(guān)于直線關(guān)于直線x=mx=m對(duì)稱，則對(duì)稱，則m= ,ym= ,y1 1=y=y2 2, ,2 2、點(diǎn)（、點(diǎn)（x,yx,y) )關(guān)于直線關(guān)于直線y=ny=n對(duì)稱的點(diǎn)的坐標(biāo)為對(duì)稱的點(diǎn)的坐標(biāo)為(x,2n-y),(x,2n-y),即若兩點(diǎn)即若兩點(diǎn)(x(x1 1,y,y1 1) )、（、（x x2 2,y,y2 2) )關(guān)于直關(guān)于直線線y=ny=n對(duì)稱，則對(duì)稱，則x x1 1=x=x2 2, n=, n=1 1、點(diǎn)（、點(diǎn)（3 3，4 4）關(guān)于直線）關(guān)于直線x=4x=4對(duì)稱的點(diǎn)

10、的坐標(biāo)對(duì)稱的點(diǎn)的坐標(biāo)是是 ，關(guān)于直線，關(guān)于直線y=-4y=-4對(duì)稱的點(diǎn)的坐標(biāo)對(duì)稱的點(diǎn)的坐標(biāo)為為 . . 221xx 221yy （5，4）（3，-12）2.2.已知，如圖，已知，如圖，ABCABC的坐標(biāo)分別為的坐標(biāo)分別為A A（-4-4，1 1），），B B（-2-2，-2-2），），C C（0 0，3 3）。作出）。作出ABCABC關(guān)于直線關(guān)于直線x=-2x=-2對(duì)稱的圖形，寫出它們對(duì)應(yīng)點(diǎn)的坐標(biāo)。對(duì)稱的圖形，寫出它們對(duì)應(yīng)點(diǎn)的坐標(biāo)。x xy yO OB BA AC C1122-1-1-2-2-4-333AA（0 0，1 1）BB（-2-2，-2-2）CC（-4-4，3 3）CCAA（BB）類似: 若兩點(diǎn)(x1，y1)、(x2，y2)關(guān)于直線y=n對(duì)稱，則 ，n= 16 歸納:若兩點(diǎn)(x1，y1)、(x2，y2)關(guān)于直線x=m對(duì)稱，則m= ， 221xx 221yy y1=y2x1=x21、學(xué)習(xí)了在平面直角坐標(biāo)系中，關(guān)于、學(xué)習(xí)了在平面直角坐標(biāo)系中，關(guān)于x軸和軸和y軸軸對(duì)稱的點(diǎn)的坐標(biāo)的特點(diǎn)。對(duì)稱的點(diǎn)的坐標(biāo)的特點(diǎn)。這節(jié)課你學(xué)到了什么？關(guān)于關(guān)于x軸對(duì)稱的點(diǎn)軸對(duì)稱的點(diǎn)橫坐標(biāo)相等橫坐標(biāo)相等,縱坐標(biāo)互為相反數(shù)縱坐標(biāo)互為相反數(shù).關(guān)于關(guān)于y軸軸對(duì)稱的點(diǎn)對(duì)稱的點(diǎn)橫坐標(biāo)互為相反數(shù)橫坐標(biāo)互為相反數(shù),縱坐標(biāo)相等縱坐標(biāo)相等.2、學(xué)習(xí)了在平面直角坐標(biāo)系中如何畫一個(gè)圖形、學(xué)習(xí)了在平面直