EBOOK bài tập HÌNH học 11 PHẦN 1 MỘNG HY (CHỦ BIÊN)

(Chu bien) KHU QUOC ANH - NGUYEN HA THANH MONGHY BAI TAP HINH HOC NHA XUAT BAN GIAO DUG VIET NAM NGUYEN M O N G HY (Chu bien) KHU QUOC ANH - NGUY^'N HA THANH BAI TAP HINH HOC 11 (Tdi bdn ldn thvC ba) C* •* NHA XUAT BAN GIAO DUC VIET NAM Ban quyen thuoc Nha xuat ban Giao due Viet Nam 01-20 lO/CXB/479-1485/GD Ma so : CB104T0 LOl NOI DAU ludn sdch BAI TAP HINH HOC 11 ducfc bien soqn nhdm giup cho hoc sinh l&p II cd them tdi lieu tu hoc vd turen luyen de nam viing cdc kien thicc vd kT ndng co bdn da duoc hoc sdch gido khoa Hinh hoc 11, tqo diiu kien gop phdn doi mai phuang phdp dqy vd hoc d trudng THFT hien Noi dung cuon sdch bdm sdt theo ngi dung cua sdch gido khoa mai, phii hap vdi chuang trinh Gido due thong mon Todn cua Bo Gido due vd Ddo tqo viia han hdnh ndm 2006 Ngi dung cudn sdch ndy gom : Chirong I : Phep ddi hinh vd phep dong dqng mat phdng Chirong II : Dudng thdng vd mat phdng khong gian Quan he song song Chuong III : Vecto khong gian Quan he vuong goc khong gian Bdi tap cudi ndm Ngi dung cudmdi chuang duac chia nhieu chii de, moi chii de Id mgt xoan (§) Trong tiing xoan, cdu true dugc trinh bdy theo thic tu nhu sau : A, Cac kien thufc can nhdf: Phdn ndy neu tdm tdt nhitng kie'n thdc ca bdn vd kf ndng ca bdn cdn nhd da dugc trinh bdy sdch gido khoa Hinh hgc 11 B Dang toan co ban : Phdn ndy he thdng lai cdc dqng todn thudng gap ldm bdi tap, neu cdc phuang phdp gidi chu yeu vd cho cdc vi du minh hoq, dong thdi cho them cdc dieu luu y cdn thiet C Cau hoi va bai tap : Phdn ndy nhdm muc dich ciing cdvd van dung kien thdc vd kT ndng ca bdn de trd ldi cdu hdi vd ldm bdi tap thugc cdc dqng vda neu d tren, tqo dieu kien cho hgc sinh ren luyen them ve phong cdch tu hgc Cudi mdi chuang co cdc bdi tap mang tinh chdt on tap vd mgt sd cdu hoi trac nghiem nhdm giiip hgc sinh ldm quen vdi mgt dqng bdi tap mdi Cudi sdch co phdn hudng ddn gidi vd ddp sd cho cdc loqi cdu hoi vd bdi tap Mac dii cdc tdc gid da cd gdng rdt nhieu, nhung chdc rdng khong th trdnh dugc cdc thieu sot Rdt mong cdc dgc gid vui ldng gop y de ch nhiing ldn tdi bdn sau, cudn sdch se dugc hodn thien tdt han CAC TAC GIA CHUtiNC I PHEP DOI HiNH VA PHEP DONG DANG TRONG MAT PHANG §1 PHEP BIEN HINH §2 PHEP TINH TIEN A CAC KIEN THUfC CAN NHd I PHEP BIEN HINH Dinh nghia Quy tdc ddt tuang dng mdi diem M cua mat phdng vdi mat diem xdc dinh nhdt M' cua mat phdng dugc ggi Id phep bien hinh mat phdng Ta thucmg ki hieu phep bie'n hinh la F va vid't F{M) = M' hay M' = F(M), diem M' duoc goi la anh cua diem M qua phep bi6i hinh F Ne'u ^ la mOt hinh nao mat phang thi ta ki hieu J ^ ' = F ( J ^ la tap cac di^m M' = F{M), voi moi dilm M thuOc ^ Khi ta noi F bien hinh ^ hinh ^jf^', hay hinh ^ ' la anh cua hinh J ^ qua phep bie'n hinh F Dl chiing minh hinh ^ ' la anh cua hinh ^ qua phep bie'n hinh F ta co thi chiing minh : Vdi dilm M y thuOc ^ thi F{M) e J^' va voi mOi M' thuOc J ^ ' thi CO M e J ^ cho F{M) =M' Phep bie'n hinh bie'n mOi dilm M cua mat phang chinh no duoc goi la phep dong nhdt IL PHEP TINH TIEN Dinh nghia Trong mat phang cho vecto v Phep bie'n hinh bie'n mOi diem M dilm M' cho MM' = V duoc goi la phep tinh tie'n theo vecta v (h.1.1) Phep tinh tie'n theo vecto v thudng duoc kf hieu la r- M' M • Hinh 1.1 Nhu vay T-(M) = M'^ MM' = v Nhdn xet Phep tinh tie'n theo vecto - khOng chinh la phep dong nhdt III, BIEU THtrc TOA D O CUA PHEP TINH TIEN Trong mat phang Oxy cho diem M(x; y), v (a ; h) Goi dilm M\x'; j') = T^ (M) Khi {x'-x + a \y=y + b IV TINH CHAT CUA PHEP TINH TIEN Phep tinh tien 1) Bao toan khoang each giira hai dilm ba!t ki; 2) Bie'n mot ducmg thang ducmg thang song song hoac trimg vdi ducmg thang da cho; 3) Bie'n doan thang doan thang bang doan thang da cho ; 4) Bie'n mOt tam giac tam giac bang tam giac da cho ; 5) Bie'n mOt dudfng tron dudmg tron co cung ban kinh B DANG T O A N CO BAN VAN ii Aac dinh anh cua mot hinh qua mot phep tinh tien Phuang phdp gidi Diing dinh nghia hoac bilu thiic toa dO cua phep tinh tien Vidu Vidu Cho hinh binh hanh ABCD Dung anh ciia tam giac />iBC qua phep tinh tie'n theo vecto /U) gidi Vi BC = AD nen phep tinh tie'n theo vecto AD bie'n dilm A dilm D, bie'n dilm B dilm C (h.1.2) Dl tim anh cua dilm C ta dung hinh binh hanh ADEC Khi anh ciia dilm C la dilm E Vay anh cua tam giac ABC qua phep tinh tie'n theo vecto AD la tam giac DCE Vidu Trong mat phang toa dO Oxy cho v = ( - ; 3) va dudng thang d co phuong trinh ?)X - 5y + 2> - Q Viet phucmg tiinh cua dudng thang d' la anh cua d qua phep tinh tie'n T- gidi Cdch La'y mOt dilm thuOc d, chang han M - {-\ ; 0) Khi M' = T^ (M) = (-1 - ; + 3) = (-3 ; 3) thuoc d' Vi d' song song vdi d nen phuong trtnh ciia nd cd dang 2>x - 5y + C = Q.Do M' & d' nen 3(-3) - + C = Tur dd suy C = 24 Vay phuong trinh cua d' la 3x-5y + IA = Cdch Tii bieu thiic toa dO ciia T^ \x' = x-2 l/ = J + suy x = x' + 2, y = y'- Thay vao phuong trtnh ciia d ta dugfc 3(x' + 2) - 5(y' - 3) + = 0, hay 3JC' - 5y' + 24 = Vay phuong trinh cua d' \&:?,x-5y + 2A = Cdch Ta cung cd thi My hai dilm phan biet M, N tren d, tim toa cac anh M', N' tuong ling ciia chiing qua T- Khi dd d' la dudng thang M'N' Vidu Trong mat phang toa dd Oxy cho dudng tron (C) cd phuong trtnh x^+y'^-2x + 4y-4 = Tim anh ciia (C) qua phep tinh tie'n theo vecto v = (-2 ; 3) gidi Cdch I Di tha'y (C) la dudng trdn tam /(I ; - 2), ban kinh r = Goi /' = r^(/) = (1 - ; - + 3) = (- ; 1) va ( O la anh cua (C) qua 7^ thi ( O la dudng trdn tam /' ban kinh r = Do dd (C) cd phuong trtnh {x+\)' + (y-\f = { X —- X ^ [JC—•X"l"2 y =y + [^ = 3^-3 '' Thay vao phucmg trtnh ciia (C) ta duoc (x' + 2) + Cy' - 3)^ - 2(x' + 2) + 4Cy' - 3) - = AFII(BCE) [BE c (BCE) Ma AD, Afi c (ADF) ntn (ADF) II (BCE) (h.2.42) b) Vi ABCD va ABEF la cac hinh vudng nen AC = BF Ta cd : MM'II CD NN'IIAB Hinh 2.42 AM' AM AD AC AN' _ BN AF ~~BF Sosanh(l)va(2)tadugc (1) (2) AM' AN' => M'N'HDF AD AF c) Tfl chung minh tren suy DF II (MM'N'N) NN'HAB^NN'IIEF] NN' c (MM'N'N) J EF II (MM'N'N) Ma DF, EF c (DEF) ntn (DEF) // (MM'N'N) Vi MN c (MM'N'N) vi (MM'N'N) H (DEF) ntn MN II (DEF) 2.25 a) Ta cd 77' // BB' va IF = BB' Mat khae AA'II BB' viAA'= BB'ntn: AA'//77'vaAA'= 77' => AA 77 la hinh binh hanh => A7//A'7'(h.2.43) h) Ta cd : \Ae(AB'C') \Ae(AAl'l) ^Ae(AB'C')r^(AAl'l) ^^^^^'^^{7'G(!^'7'7)="''^(^'^'> ' Hinh2.43 95 => 7'G (AB'O n (AA'7'7) ^ (AB'C) n (AA'7'7) =A7' Dat A ' n A = fi Tacd: ^ ^ ^ ^ ^ , ^ £ e ( A ' C ' ) vay E la giao dilm cfla A va mat phing (AB'C) c)Tacd:A'fi n Afi' = M = Tuong tu: AC n A'C = A^ \M G (AB'C) [M G (ABC) \N e (AB'C) [N e (ABC) Vay (AB'O n (A'BC)=MN 2.26 a) Ta cd tfl giac AA'CC la hinh binh hanh (h.2.44) suy A'C cit AC tai trung dilm cfla mdi dudng Do dd 777 // CB' (dudng trung binh cfla tam giac CB'A') Mat khae 777 c (A77C0 ndn CB // (A77C0 b) Ta cd: fAG(AS'G') lAG(AfiC) A la dilm chung cfla (AB'C) va (ABC), B'C IIBC ma MCC w A7fifi' (h.2.59) ^ IB BE' _h Ic" CC'~ c CC'HAA' => UCC => A'AIIBB' ^ ^ w A7AA' 7C CC c = 7= -7A AA a ^KAA'[...]... cflng ban kfnh 1 ^ Chd y Gia su phep quay tam I gdc a bien dudng thing d thanh dudng thing d' (h 1. 14) Khidd ^ 7t - Ndu 0' + 15 = 0 Hay xac dinh toa dd cac dinh cua tam giac A'B'C va phuong trtnh cua dudng thing d' theo thfl tu la anh cua tam giac ABC va dudng thing d qua phep quay tam O, gdc quay 90° 24 1. 17, Cho nfla dudng trdn tam O dudng kinh BC Dilm A chay trdn nfla dudng trdn dd Dung vl phfa ngoai cua tam giac ABC hinh vudng ABEF Chung minh ring E chay tren mdt nfla dudng trdn cd dinh 1. 18 Cho tam giac