Cau 11 • Cho AABC ndi tiep dudng trdn tam O, // la true tam AABC, D la diem dd'i xiing ciia A qua O Khi dd HA + WB + ITc bdng (a)//0 (h)lHO (c)3H0 (6) 4H0 Trd ldi: Phuang an dung : (b) §5 True toa va he true toa (tiet 12,13,14) MUC TIEU Kie'n thurc Nhan biet dupe toa dp cua vecto, toa dp ciia diem dd'i vdi true tpa dp va he true tpa dp Hpc xong phan nay, hpc sinh cdn xac dinh dupe toa dp ciia vecto va cua diem, hieu va nhd dupe bieu thifc toa dp cua cac phep toan ve vecto, cac cdng thiic bieu thi quan he giita eac vecto (cimg phuang) Hpc sinh cung can hieu va nhd dupe cac cdng thiic bieu thi quan he giiia cac diem : dieu kien de ba die'm thang hang, toa dp trung diem ciia doan thang va toa dp trpng tam ciia tam giac KT nang • Ve kl nang, hpc sinh biet each lua chpn cdng thiic thfch hpp giai toan va tfnh toan chfnh xac • Biet phan tfch mdt vecta to hop ciia cac vecto khac bdng toa dp • Chiing minh dupe mdt sd bai toan cd lien quan den trung diem, trpng tam nhd toa dp Thai dp • Lien he dupe vdi nhieu va'n de cd thuc te' • Cd mdi lien he chat che giira vecto va toa dp cua nd 72 • Viing vang tu logic II CHUXN BI CUA GV VA M Chuan bi cua GV: - GV chudn bi sdii hinh ve tii hinh 29 de'n hinh 31 SGK - Thudc ke, phab mau, Chuan bi cua HS : - HS dpc trudc bai hpc m PHAN PHOI TH6I LUONG Bai gom tiet Tiet thur nha't: Tir dau den het muc Tiet thur hai: Tiep theo den het muc Tie't thur 3: Phan cdn Iai va hudng ddn bai tap IV TIEN TDINIi DAY HOC n KI€M TRR ISni CU Cau hoi Cho hinh binh hanh ABCD ; O la tam a) Tfnh AB + AD theo AO b) Hay so sanh hai vecto AB + AD va CO Cau hoi Cho diem A, B, C Gpi G la trpng tam tam giac ABC, M la diem bat ki Tfnh tdng MB + MC + MC 73 Bni MOI HOAT DONG 1 True toa a) Mtic dich: Giiip HS hieu dugc tog eua vecto trin true, ddi dgi so b) Hudng thuc Men - Ddt vd'n di' - Thue Men ^\^ - Trinh bdy ve ddi dgi so c) Qud trinh thuc Men • Dat van de GV ve hinh 27 va thirc hien cac thao tac sau: - Neu khai niem true toa dp: True va vecta don vi - Kf hieu true toa dp - Toa dp cua vecto tren true a x' * T I Hinh 27 • Thuc hien ^ ^ GV thu'c hien thao tac 5' Hoat ddng cua GV Cdu hdi Hoat ddng ciia HS Ggi y trd ldi cdu hdi Vecto OA cd toa dp bang bao nhieu? Vecto OA cd toa dp bdng toa dp cua A va bang a 74 Ggi y trd ldi edu hdi Cdu hdi Vecto OB ed toa dp bdng bao nhiau? Vecto OB c6 toa dp bdng toa dp eua B va bdng b Ggi y trd ldi cdu hdi Cdu hdi Hay bieu dian vecto AB qua hai jB = aB-aA^b-a vecto OA v a Cdu hdi Ggi y trd ldi edu hdi Gpi / la trung diem AB Tim toa Toa dp cua / bdng dp cua / • Do dai dai sd cua vecta tren true GV nau dinh nghia: Ni'u hai diem A, B nam trin true Ox thi tog eua vecto AB dugc ki Mill la AB vd ggi Id ddi dgi sd cda vecto AB trin true Ox Nhu vdy, AB = AB i GV neu hai nhan xet sau: 1) Hai vecto AB va CD bdng va chi AB = CD (hien nhien); 2) He thii'c AB + BC = AC tuong duong vdi he thifc AB + BC = AC (he thiic Sa-lo) GV cho HS thyc hien thao tac sau 3' de cung co kien thCrc Hoat-ddng ciia GV Cdu hdi Cho A cd toa dp la a, B cd toa dp la Hoat ddng ciia HS Ggi y trd ldi edu hdi b-a B Tim dp dai dai sd ciia AB 75 Cdu hdi Tim dp dai dai sd eiia AI (vdi / la trung diem ciia AB) HOAT DONG 2 He true toa a) Muc dich: Giiip HS nam duge hi true tog dgvd van dung gidi todn b) Hudng thuc Men - GV niu he true tog c) Qud trinh thuc Men • GV gidi thieu ve he true toa thdng qua hinh 28 SGK _> J —> i x Hinh 28 • GV gidi thieu he true toa dp, mdi lien he vdi cac he true da hoc GV neu cau hoi HI Toa dp ciia diem va toa dp cua vecto ed lien quan nhu the' nao? H2 He true toa dp cd lien quan nhu the' nao vdi true toa dp ? 76 HOAT DONG 3 Toa cua vectd doi v6i he true toa a) Muc dich: Giiip HS tim dugc tog cua vecto, cua diem b) Hudng thuc Men -Thitc Men ^ f - GV neu dinh nghia trang 27 SGK Thuc hiin ? - Niu nhdn xit trang 27 SGK c) Qud trinh thitc Men • Thuc hien ' ^ - Treo hinh 29 len bang yn ^ Hinh 29 GV thirc hien thao tac 5' Hoat ddng cua GV Hoat ddng cua HS Ggi y trd ldi cdu hoi Cdu hdi Hay bieu thi vecta a qua i va j - ^- 5- a-ll+— I Cdu hdi Hay bieu thi vecto b qua i va j Ggi y trd ldi cdu hdi b = -3l+0j Ggi y trd ldi edu hdi Cdu hdi Hay bieu thi vecto u qua / va j ^^ u = li — 3^ / Ggi y trd ldi cdu hdi Cdu hdi Hay bieu thi vecto v qua / va j v = Oi + - j • Neu dinh nghia Ddi vdi hi true tog dd(0 ; i,j), ni'u d = xi+yj thi cap sd (x ; y) di'or: [joi Id toe cua vecto a, ki Men Id a = (x ; y) hay a (x ; y) Sd tint nhdt x ggi Id hodnh do, so thic hai y ggi la tung ctia vecto a • Thuc hien ? GV thirc hien thao tac 5' 78 Hoat ddng ciia HS Hoat ddng ciia GV Ggi y trd ldi cdu hdi Cdu hdi Xac dinh toa dp cua cac vecto a^(l a, b, U, V trin hinh 29 ; -) ; b = (-3 ;0) t u = (l; ) Cdu hdi ; v = (0;-) Ggi y trd ldi edu hdi Dd'i vdi hi tnic tog (0 ; i ,j), i = OA, dd A la diem (1 ; 0) hdy chi tog ciia ede vecto 0, i , j , i + j , Ij-i y = Ofi, dd 5(0 ; 1) ; / + y = OC, ddC(l ; 1) -7-3j,V3 7+0,14) 2j-i = 0D, dd D(-l ; 2); - / - = / ^ , ddA:(- ;-3) V3 7+ 0,14y = OM, dd M(S ;0,14) • Neu nhan xet Tii dinh nghia toa dp ciia vecta, ta thay hai vecto bdng va chi chung cd ciing toa dp, nghia la d(x; y) = b(x'; y')[...]... => 7]V = (-1 - x ; 3 - y) 7M=(3-x ;2- y) 105 _ _ 3-x = 3f-l-xj IM = 3IN - • I b) MNPQ la hinh binh hanh, sny ra MN = QP Gia sir Q(x ; y), trong dd MN=(-4;l); QP = (-1 - x ; I - y).Do ¥N = QP ^ I - 2 - x = - 4 ^ [^^ = 2 [l-y = l [y = 0 vay (2( 2 ; 0) e) M7V=(-4; 1); MP=(-5;-l), NP = (-l ; -1) 3MN + 2MP =(-11 ;l)va 2MN-3NP=(-5 106 ; 8) CkiroNQ II CUA HAI VECTd... BA = AC-AB b) AB + AC = 2AM = BC AC + BA AB + AC = 1 AM BC = a = aS c) (BG + CG) = -(GB + GC) = 2GM: BG + CG = 2 GM Cdu 2 MN=MA+AD+DN MN=MB+BC+CN => 2MN = AD + BC Cdu 3 2BM = 2BA + 2AM BM=BC+CM Cdng ve' vdi ve' ta dupe 3BM = 1BA + BC^ BM=-a 3 + -b 3 Cdu 4 a) A B = ( - 2 ; - 6 ) ; A G = ( 2 ; - 1 ) AG khdng cung phuang vdi AB =:> A, S, G khdng thang hang, b) Gia sit C(x ; y) 1 02 aS Tacd ^ -^G >'A+>'g+yc... Chiing minh rang /, J, K thang hang Hifdng dan C5M 7 a) AB= (-3 ; 1), AC= (-4 ; - 2 ) AB khdng ciing phuong AC Tiir dd suy ra A, B, C khdng thang hdng b) ABCD la hinh binh hanh khi va chi khi AB = DC 103 Gia sir D(x ; y) ^ DC = ( -2 - x ; -1 - y) Ta lai ed AB = (-3 ; 1) nen -2- x = - 3 [-l-y =l fx = 1 [y = - 2 VayD(l; -2) Cdu 2 a)Tac6: JA + JB = 2IM ; => JA+JB+JC+TD JC + JD = ITN = 1(JM+JN) =O h) KA + KB +... (x;y), tacd 1 + 4+ -y -2= 3 y Suyra D = (8 ; - 11) A^ = f6 ; 3j , CE = (x-l ; y + 1) Tii giac ABCE la hinh binh hanh khi va chi khi AB + CE = 0 6 + x - 2 = 0 va 3 + y - 2 = 0 Vay E = (-4; hay -1) MQT SO Bfil T6P TRfiC NGHIEM Chpn phuong an tra ldi diing Cau 1 Cho AABC cd A(l ; 2) , B(-l; 1) va C(3 ; 3) Trpng tam G eiia tam giac la (a)G (c)G r? A •3 V3 J ("^ u (b) G \ •1 (d)G J fl V3 \ 2 ) f3 \ U J — ;3 Trd... = 2 ^ 1+y va 4 = - 1 vay D = (-7 ; 1) Bai 35 Hudng ddn HS dn tap lai phdn dd'i xu:ng true va dd'i xiing tam 89 DS • Mi(x;-y),M2(-x;y),M3(-x;-y) Bai 36 Hudng ddn-gidi HS dn tap lai cdng thirc toa dp trpng tam Toa dp hai vecto bdng nhau Gidi a) Ta ed : -4 + 2 + 2 3 Trpng tam cua tam giac ABC la G 1 + 4 -2 3 hay G(0 ; 1) b) Gia sii D = (x ; y) Diem C la trpng tam tam giac ABD khi va ehi khi -4+1+x 2= ... b) Gia sit C(x ; y) 1 02 aS Tacd ^ -^G >'A+>'g+yc r_i + ('_3j + ;c = 3 fx = 7 „ '^l2-4 +y=3 ly = 5 = y^ vayC(7;5) Dfi SO 2 (45') Cdu 1 (3 didm) Trong mat phang toa dd Oxy, cho 3 didm A (2 ; 1), B(-l ; 2) va C( -2 ; -1) a) Chiing minh rang A,B,C khdng thang hang b) Tun toa dd didm D dd tir giac ABCD la hinh binh hanh Cdu 2 (3 didm) Cho tii giac ABCD, M va N tuong iing la cac trung didm ciia AB va CD, I... (b) Cau 2 Cho A( -2 ; 1), B(3 ; 1) dp dai vecto A5 la 90 (a) 5; (b) V26 (c)V27; (d)V24 Trd ldi: Phuang an diing : (b) Cau 3 Trong mat phdng toa dp Oxy cho C(l ; 0) Dung hinh binh hanh 0A6C khi dd : (a) Tung dp vecto AB bdng 0 (b) Hoanh dp vecto AB bdng 0 (C) X^ + XQ + XC + XO = 0 (d) A va 5 cd tung dp khac nhau Trd ldi: Phuong an dung : (a) Cau 4 Trong mat phdng toa dp Oxy cho 4 diem : A(0 ; 1), B(l... (e) 7 Trd ldi Chpn (a) 8 Trd ldi Chpn (b) 9 Trd ldi Chpn (b) 10 Trd ldi Chpn (a) II Trd ldi Chpn (c) 12 Trd ldi Chpn (d) 13 Trd ldi Chpn (d) 14 Trd ldi Chgn (a) 15 Trd ldi Chpn (d) 16 Trd ldi Chpn (b) 17 Trd ldi Chpn (d) 18 Trd ldi Chpn (b) 19 Trd ldi Chpn (d) 20 Trd ldi Chpn (a) 21 Trd ldi Chpn (b) 22 Trd ldi Chpn (b) 23 Trd ldi Chpn (b) 100 HOATDONG^ G(?l Y MQT SO OE KIEM TRfl CHCTONG I a) Muc dich:... AC Trd ldi: Phuong an diing : (e) Cau 9 Cho A(l ; 1), B(3 ; 2) , C(m + 4 ; 2m + 1) De A, B, C thang hang thi: (a) m= I; (b) m = 2 (e) m = 3; (d) m = 0 Trd ldi: Phuong an diing : (a) Cau 10 Cho tam giac deu ABC canh a Chpn he toa dp Oxy nhu hinh ve Toa dp tam dudng trdn ngoai tiep AABC la : aS (a)(0;^a); (b) (c) 0; (d) 0; Trd ldi: Phuang an diing : (c) 92 ;0 aS On tap chvtdng I (tie1t 13,14) I MUC TifiU... - \ e =(0,15; 1,3), V 2 2; 87 / = (7t; - cos24°) Bai 31 GV hudng ddn cdu a) Hoat ddng ciia GV Hoat ddng ciia HS Ggi y trd ldi cdu hdi 1 Cdu hdi 1 la=(4 Hay tim toa dp cac vecto la, - 3b Ggi y trd ldi cdu hdi 2 Cdu hdi 2 Tim ;1), -3b =( - 9;- 12) toa dp ciia u= (l;-S) vecto M = 25 - 3^7 + c Trd ldi cdc cdu cdn lgi h)x + d = b-cox = -d + b-c Suy ra x = (-6 ; 1) e) Tim toa dp cua vecto k d + l b rdi so ... Trd ldi Chpn (d) 18 Trd ldi Chpn (b) 19 Trd ldi Chpn (d) 20 Trd ldi Chpn (a) 21 Trd ldi Chpn (b) 22 Trd ldi Chpn (b) 23 Trd ldi Chpn (b) 100 HOATDONG^ G(?l Y MQT SO OE KIEM TRfl CHCTONG I a) Muc... = AC-AB b) AB + AC = 2AM = BC AC + BA AB + AC = AM BC = a = aS c) (BG + CG) = -(GB + GC) = 2GM: BG + CG = GM Cdu MN=MA+AD+DN MN=MB+BC+CN => 2MN = AD + BC Cdu 2BM = 2BA + 2AM BM=BC+CM Cdng ve'... C(x ; y) 1 02 aS Tacd ^ -^G >'A+>'g+yc r_i + ('_3j + ;c = fx = „ '^l2-4 +y=3 ly = = y^ vayC(7;5) Dfi SO (45') Cdu (3 didm) Trong mat phang toa dd Oxy, cho didm A (2 ; 1), B(-l ; 2) va C( -2 ; -1)