人教版九年級(jí)(上)數(shù)學(xué)教學(xué)課件第23章

旋轉(zhuǎn)23.2.3

關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)情境導(dǎo)入探究新知當(dāng)堂訓(xùn)練典例精講知識(shí)歸納情境導(dǎo)入溫故知新關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)第一象限第三象限第二象限第四象限y的負(fù)半軸上x的負(fù)半軸上下列各點(diǎn)分別在坐標(biāo)平面的什么位置上？A(3,2)B(0,-2)C(-3,-2)D(-3,0)E(-1.5,3.5)F(2,-3)(＋,＋)(0，y)(－,－)(x，0)(－,＋)(＋,－)關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)01坐標(biāo)系中的中心對(duì)稱02知識(shí)要點(diǎn)精講精練A′【問題】求點(diǎn)A(2,1)關(guān)于原點(diǎn)對(duì)稱的點(diǎn)A′坐標(biāo)？xO123-1-2-312-1-2-3yA∴A′(-2,-1)BB′易證△ABC≌△A′B′C′思考:關(guān)于原點(diǎn)對(duì)稱的兩個(gè)點(diǎn)的坐標(biāo)之間有什么關(guān)系?知識(shí)點(diǎn)一探究新知關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)解：連接AO并延長(zhǎng)至A′使OA′=OA,作AB⊥x軸于點(diǎn)B,A′B′⊥x軸于點(diǎn)B′.橫坐標(biāo)、縱坐標(biāo)的符號(hào)都互為相反數(shù)，點(diǎn)P(a,b)關(guān)于x軸對(duì)稱的點(diǎn)的坐標(biāo)為P′(a,-b)；簡(jiǎn)記為：誰對(duì)稱，誰不變,原點(diǎn)對(duì)稱都改變.點(diǎn)P(a,b)關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)為P′(-a,b).點(diǎn)P(a,b)關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)為P′(-a,-b)；【例1】如圖,在邊長(zhǎng)為1的正方形組成的網(wǎng)格中,每個(gè)正方形的頂點(diǎn)稱為格點(diǎn).已知△AOB的頂點(diǎn)均在格點(diǎn)上,建立如圖所示的平面直角坐標(biāo)系,點(diǎn)A、B的坐標(biāo)分別是A(3,2),B(1,3).(1)畫出△AOB關(guān)于原點(diǎn)O對(duì)稱的圖形△A1OB1,并寫出點(diǎn)A1,B1的坐標(biāo).(2)將△AOB繞點(diǎn)O逆時(shí)針旋轉(zhuǎn)90o得到△A1OB1,并寫出點(diǎn)A2,B2的坐標(biāo).xyOABA2B2A1B1易錯(cuò)提示:作旋轉(zhuǎn)圖形不要搞錯(cuò)方向.解:(1)點(diǎn)A1的坐標(biāo)為_______,點(diǎn)B1的坐標(biāo)為_______.知識(shí)點(diǎn)一典例精講關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)(2)點(diǎn)A2的坐標(biāo)為_______,點(diǎn)B2的坐標(biāo)為_______.(-2,3)(-3,1)(-3,-2)(-1,-3)1.若(a-2,3)和(-1,b+2)關(guān)于原點(diǎn)對(duì)稱,則(a,b)在()A.第二象限B.第一象限C.第四象限D(zhuǎn).第三象限2.若a＜0,則點(diǎn)P(a2,-a)關(guān)于原點(diǎn)的對(duì)稱點(diǎn)P1在第_____象限.3.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)于原點(diǎn)對(duì)稱,則a=_____，b=_______.4.已知點(diǎn)M(1-2m,m-1)關(guān)于原點(diǎn)的對(duì)稱點(diǎn)在第一象限,則m的取值范圍在數(shù)軸上表示正確的是()C三-1.2-5.6知識(shí)點(diǎn)一針對(duì)訓(xùn)練關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)C00.5A100.5B100.5C100.5D15.如圖,將線段AB繞點(diǎn)O順時(shí)針旋轉(zhuǎn)90o得到線段A′B′,那么A(-2,5)的對(duì)應(yīng)點(diǎn)A′的坐標(biāo)是______.6.如圖,在平面直角坐標(biāo)系中,點(diǎn)A和點(diǎn)B的坐標(biāo)分別為(2,0),(0,-4),若將線段AB繞點(diǎn)A順時(shí)針旋轉(zhuǎn)90o得到線段AC,則點(diǎn)C的坐標(biāo)為______.(5,2)AxyOB′A′B知識(shí)點(diǎn)一拓展提升關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)(-2,2)CxyOAB關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)01坐標(biāo)系中的中心對(duì)稱02知識(shí)要點(diǎn)精講精練解：△ABC的三個(gè)頂點(diǎn)A(-4,1),B(-1,-1),C(-3,2)關(guān)于原點(diǎn)的對(duì)稱點(diǎn)分別為A′(4,-1),B′(1,1),C′(3,-2)依次連接A′B′,B′C′,C′A′，就可得到與△ABC關(guān)于原點(diǎn)對(duì)稱的△A′B′C′.【例2】如圖,利用關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)的特點(diǎn),作出△ABC關(guān)于原點(diǎn)對(duì)稱的圖形.A(-4,1)C(-3,2)B(-1,-1)B′(1,1)C′(3,-2)A′(4,-1)yxO作關(guān)于原點(diǎn)的中心對(duì)稱圖形的步驟：(1)寫：寫出圖形頂點(diǎn)坐標(biāo)；(2)求：求出各點(diǎn)關(guān)于原點(diǎn)對(duì)稱的點(diǎn)坐標(biāo)；(3)描：在坐標(biāo)系內(nèi)描出這些對(duì)稱點(diǎn)的位置；(4)連：順次連接各點(diǎn)即為所作的對(duì)稱圖形；(5)答：寫下結(jié)論.知識(shí)點(diǎn)二典例精講坐標(biāo)系中的中心對(duì)稱xyO-5-4-3-2-112345-12341-2-31.四邊形ABCD各頂點(diǎn)的坐標(biāo)分別為A(5,0),B(-2,3),C(-1,0),D(-1,-5),作出與四邊形ABCD關(guān)于原點(diǎn)O對(duì)稱的圖形-4-55ABCD知識(shí)點(diǎn)二針對(duì)訓(xùn)練坐標(biāo)系中的中心對(duì)稱2.如圖,直線a⊥b于點(diǎn)O,點(diǎn)A與點(diǎn)A′關(guān)于直線a對(duì)稱,點(diǎn)A′與點(diǎn)A″關(guān)于直線b對(duì)稱,點(diǎn)A與點(diǎn)A″有怎樣的對(duì)稱關(guān)系?你能說明理由嗎?baA″A′AOBC提升能力強(qiáng)化訓(xùn)練坐標(biāo)系中的中心對(duì)稱證明OA=OA″,∠AOA″=180o2.如圖,直線a⊥b于點(diǎn)O,點(diǎn)A與點(diǎn)A′關(guān)于直線a對(duì)稱,點(diǎn)A′與點(diǎn)A″關(guān)于直線b對(duì)稱,點(diǎn)A與點(diǎn)A″有怎樣的對(duì)稱關(guān)系?你能說明理由嗎?baA″A′AO提升能力強(qiáng)化訓(xùn)練坐標(biāo)系中的中心對(duì)稱以b為x軸,a為y軸建立平面直角坐標(biāo)系.設(shè)點(diǎn)A的坐標(biāo)為(m,n)∵點(diǎn)A與點(diǎn)A′關(guān)于直線a對(duì)稱,∴點(diǎn)A′的坐標(biāo)為(-m,n)∵點(diǎn)A′與點(diǎn)A″關(guān)于直線b對(duì)稱,∴點(diǎn)A″的坐標(biāo)為(m,-n)∴點(diǎn)A與點(diǎn)A″關(guān)于點(diǎn)O對(duì)稱.解：∴點(diǎn)A與點(diǎn)A″關(guān)于點(diǎn)O對(duì)稱.理由如下：3.如圖所示,OA的長(zhǎng)為2,將△ABC繞點(diǎn)A旋轉(zhuǎn)180o后,得△AB′C′,若點(diǎn)B的坐標(biāo)為(a,b),則點(diǎn)B′的坐標(biāo)為