用坐標(biāo)表示軸對(duì)稱 (3)

1、2 2、畫一個(gè)圖形關(guān)于、畫一個(gè)圖形關(guān)于x x軸或軸或y y軸的對(duì)稱圖軸的對(duì)稱圖形形1 1、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)（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_._.AAMN 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延長(zhǎng)延長(zhǎng)AOAO至至OAOA, ,使使AO=OAAO=OA. .過點(diǎn)過點(diǎn)A A作作AOAOMNMN于于O O點(diǎn)，點(diǎn)，思思考考然后然后依據(jù)是什么？依據(jù)是什么？探究探究1 1：如圖，在平面直角坐標(biāo)系中你能：如圖，在平面直角坐標(biāo)系中你能畫出點(diǎn)畫出點(diǎn)A A、B B

2、、C C關(guān)于關(guān)于x x軸的對(duì)稱點(diǎn)嗎軸的對(duì)稱點(diǎn)嗎? ?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？xyA (2,3)A(2,-3)練習(xí)練習(xí): :1 1、點(diǎn)、點(diǎn)P(-4, 5)P(-4, 5)與點(diǎn)與點(diǎn)Q Q關(guān)于關(guān)于x x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_._.2 2、點(diǎn)、點(diǎn)M(aM(a, -3), -3)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 =_

3、.=_.(-4 , -5 )-23探究探究2 2：如圖，你能在平面直角坐標(biāo)系中：如圖，你能在平面直角坐標(biāo)系中畫出點(diǎn)畫出點(diǎn)A A、B B、C C關(guān)于關(guān)于y y軸的對(duì)稱點(diǎn)嗎軸的對(duì)稱點(diǎn)嗎? ?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？xyA (2,3)A(-2,3)練習(xí)練習(xí): :1 1、點(diǎn)、點(diǎn)P(-5, 4)P(-5, 4)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_._.2 2、點(diǎn)、點(diǎn)M(

4、aM(a, -2), -2)與點(diǎn)與點(diǎn)N(-3, b)N(-3, b)關(guān)于關(guān)于y y軸對(duì)軸對(duì)稱，則稱，則a=_, b =_.a=_, b =_.( 5 , 4 )3-2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)（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, y)( x, y)A.1、完成下表、完成下表.已知點(diǎn)已知點(diǎn)(1,-2)(-4,3)(-6,-7)(5,1)(9, 0)關(guān)于關(guān)于x軸的對(duì)稱點(diǎn)軸的對(duì)稱點(diǎn)關(guān)于關(guān)于y軸的對(duì)稱點(diǎn)軸的對(duì)稱點(diǎn)(-1, -2)(1,2)(-4,-3)(4, 3)(6, -7)(-6,7

5、)(-5, 1)(5,-1)(-9,0)(9,0)B.2、已知點(diǎn)、已知點(diǎn)P(6, 2)與點(diǎn)與點(diǎn)P(b, -a).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=_.練練 習(xí)習(xí)26-2-6A.1、完成下表、完成下表.已知點(diǎn)已知點(diǎn)(2,-3)(-1,2)(-6,-5)(0.5,1)(4, 0)關(guān)于關(guān)于x軸的對(duì)稱點(diǎn)軸的對(duì)稱點(diǎn)關(guān)于關(guān)于y軸的對(duì)稱點(diǎn)軸的對(duì)稱點(diǎn)(-2, -3)(2,3)(-1,-2)(1, 2)(6, -5)(-6, 5)(-0.5, 1)(0.5,-1)(-4,0)(4,0)B.2、已知點(diǎn)、已知點(diǎn)P(6, b

6、+2)與點(diǎn)與點(diǎn)P(a+b, -3a).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=_.練練 習(xí)習(xí)242-8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 A(3,5), (3,5), B B(4,1),C(4,1),C(1,3).(1,3).依次依次連接連接A AB B,B,BC C,C,CA A, ,就得就得到到ABCABC關(guān)于關(guān)于y y軸對(duì)稱的軸對(duì)稱的A AB BC C. .A31425-2

7、-4-1-301 2 3 4 5-4 -3 -2 -1cBBAC歸納歸納: :對(duì)于這類問題對(duì)于這類問題, ,只要先求只要先求出已知圖形中的一些特殊點(diǎn)出已知圖形中的一些特殊點(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), ,就可就可以得到這個(gè)圖形的軸對(duì)稱圖形以得到這個(gè)圖形的軸對(duì)稱圖形. .xy 練習(xí)練習(xí): (1,2)2 2、在平面直角坐標(biāo)系中一個(gè)圖形關(guān)于、在平面直角坐標(biāo)系中一個(gè)圖形關(guān)于x x軸軸或或y y軸的對(duì)稱圖形的畫法。軸的對(duì)稱圖形的畫法。先先求出已知圖形中的一些特殊點(diǎn)求出已知圖形中的一些特殊點(diǎn)( (如多邊形的頂點(diǎn)如多邊形的頂點(diǎn))

8、 )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), ,就可以得到這就可以得到這個(gè)圖形的軸對(duì)稱圖形個(gè)圖形的軸對(duì)稱圖形. .1.1.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)（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, y)( x, y)如圖如圖,分別作出點(diǎn)分別作出點(diǎn)P,M,N關(guān)于直線關(guān)于直線x=1的對(duì)稱點(diǎn)的對(duì)稱點(diǎn), 你能發(fā)現(xiàn)它們坐標(biāo)你能發(fā)現(xiàn)它們坐標(biāo)之間分別有什么關(guān)系嗎之間分別有什么關(guān)系嗎?31425-2-4-1-3012345-4-3-2-1x=1P(-2,3)M(-1,1)N(5,-2)N(-3,-2)M(3,1)P(4,3)xy課后思考課后思考:1、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,y)關(guān)于直線關(guān)于直線x=1對(duì)稱點(diǎn)的坐標(biāo)是多少對(duì)稱點(diǎn)的坐標(biāo)是多少?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, y)關(guān)于直線關(guān)于直線x=-1對(duì)稱點(diǎn)的坐標(biāo)是多少對(duì)稱點(diǎn)的坐標(biāo)是多少? 3、在平面直角坐標(biāo)系中、在平面直