12.2.2用坐標(biāo)表示軸對(duì)稱課件

12.2.2用坐標(biāo)表示軸對(duì)稱課件()八年級(jí)數(shù)學(xué)上冊(cè)12.2.2用坐標(biāo)表示軸對(duì)稱

學(xué)習(xí)目標(biāo)：

1、掌握在平面直角坐標(biāo)系中，關(guān)于x軸和y軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn)，并能運(yùn)用它解決簡(jiǎn)單的問題；

2、能在平面直角坐標(biāo)系中畫出一些簡(jiǎn)單的關(guān)于x軸和y軸的對(duì)稱圖形。動(dòng)動(dòng)手畫一畫

已知點(diǎn)A和一條直線MN，你能畫出這個(gè)點(diǎn)關(guān)于已知直線的對(duì)稱點(diǎn)嗎?AA’MN∴A′就是點(diǎn)A關(guān)于直線MN的對(duì)稱點(diǎn)。O然后延長(zhǎng)AO至OA′,使AO=OA′.過點(diǎn)A作AO⊥MN于O，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？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).31425-2-4-1-3012345-4-3-2-1B(-4,2)··C(3,-4)·B′(-4,-2)·C′(3,4)思考：關(guān)于x軸對(duì)稱的點(diǎn)的坐標(biāo)具有怎樣的關(guān)系？

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)相等,縱坐標(biāo)互為相反數(shù).練習(xí):1、點(diǎn)P(-5,6)與點(diǎn)Q關(guān)于x軸對(duì)稱，則點(diǎn)Q的坐標(biāo)為__________.2、點(diǎn)M(a,-5)與點(diǎn)N(-2,b)關(guān)于x軸對(duì)稱，則a=_____,b=_____.(-5,-6)-25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)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？

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).31425-2-4-1-3012345-4-3-2-1B(-4,2)··C(3,-4)·B′(4,2)·C′(-3,-4)思考：關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)具有怎樣的關(guān)系？歸納：關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)的特點(diǎn)是:橫坐標(biāo)互為相反數(shù),縱坐標(biāo)相等.練習(xí):1、點(diǎn)P(-5,6)與點(diǎn)Q關(guān)于y軸對(duì)稱，則點(diǎn)Q的坐標(biāo)為__________.2、點(diǎn)M(a,-5)與點(diǎn)N(-2,b)關(guān)于y軸對(duì)稱，則a=_____,b=_____.(5,6)2-5小結(jié)：在平面直角坐標(biāo)系中，關(guān)于x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y軸對(duì)稱的點(diǎn)橫坐標(biāo)互為相反數(shù),縱坐標(biāo)相等.點(diǎn)（x,y）關(guān)于x軸對(duì)稱的點(diǎn)的坐標(biāo)為______.點(diǎn)（x,y）關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)為______.(x,－y)(－x,y)1、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)P(2a+b,-3a)與點(diǎn)P′(8,b+2).若點(diǎn)p與點(diǎn)p′關(guān)于x軸對(duì)稱，則a=_____b=_______.若點(diǎn)p與點(diǎn)p′關(guān)于y軸對(duì)稱，則a=_____b=_______.練習(xí)246-20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軸和x軸對(duì)稱的圖形。解：點(diǎn)A(-3,5),B(-4,1),C(-1,3)，關(guān)于y軸對(duì)稱點(diǎn)的坐標(biāo)分別為A′(3,5),B′(4,1),C′(1,3).依次連接A′B′,B′C′,C′A′,就得到△ABC關(guān)于y軸對(duì)稱的△A′B′C′.····A31425-2-4-1-3012345-4-3-2-1··cBB′A′C′歸納:對(duì)于這類問題,只要先求出已知圖形中的一些特殊點(diǎn)(如多邊形的頂點(diǎn))的對(duì)應(yīng)點(diǎn)的坐標(biāo),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.探究3: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?31425-2-4-1-3012345-4-3-2-1x=1······P(-2,3)M(-1,1)N′(5,-2)N(-3,-2)M′(3,1)P′(4,3)思考:

1、在平面直角坐標(biāo)系中,點(diǎn)(x,y)關(guān)于直線x=1對(duì)稱點(diǎn)的坐標(biāo)是多少?

2、在平面直角坐標(biāo)系中,點(diǎn)(x,y)關(guān)于直線x=-1對(duì)稱點(diǎn)的坐標(biāo)是多少?

3、在平面直角坐標(biāo)系中,點(diǎn)(x,y)關(guān)于直線y=1對(duì)稱點(diǎn)的坐標(biāo)是多少?

4、在平面直角坐標(biāo)系中,點(diǎn)(x,y)關(guān)于直線y=-1對(duì)稱點(diǎn)的坐標(biāo)是多少?

(-x+2,y)(-x-2,y)(x,-y+2)(x,-y-2)1、學(xué)習(xí)了在平面直角坐標(biāo)系中，關(guān)于x軸和y軸對(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x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y軸對(duì)稱的點(diǎn)橫坐標(biāo)互為相反數(shù),縱坐標(biāo)相等.2、學(xué)習(xí)了在平面直