Ôn tập Hình học 11. chương 1

 .  !"#$%&'()!*+#,-,#.&&(/$ 0%!1#2&  &(/$M, N 345%%&(/$M’, N’ %M’N’ = MN. -,%6,0%,7&8 &(/$%9##%&(/$%9## :!"#$%&'()%;%<&(/$(=1 (4#%9#%(4#%9#1  %&%%&1 (*>%9#%(*>%9#?#=1 #=,%#=,?#=1  %&$#-,%%&$#-,?#=1 (4#%@A%(4#%@A,=,B#- !6C  -,,D%/8  %E% 8@*#$F%9#1,*:,%G ( ) Hv a b r C%E% %I*:, %G ( ) Hv a b r  1 $J%(/$K%$J%(/$KLM&*,* NMM v = uuuuur r OPQ8 v T r C R/%;,%S&(J8 @*#$F%9#TU',*KVUH'WHXV&1WC SK Y VU Y H'  WZ   : VKW!(=8U Y ZU[& ' Y Z'[ \ ]&'@*#$F%9#,*(/$,^(E:#=,45##-, α !"#()C   (/$%(/$1 (/$K!-,%(/$KLM&*,* KZKL:#=,VKHKLWZ α C_45,#S]&'%$#=,]&' α C !6Q`V 1 α W a]&'4G##45,,a]&',7&!$(b#bV[W a]&'$%@B#,a]&',7&!$(b#bVW cR/%;,%S&(J,7&]&',=%$V&HW(/$KVUH'W1(/$KLVULH'LW:#=, ]&' α 8 Trong mặt phẳng tọa độ Oxy cho Q (I, α W 1với I(a; b). Khi đó Q (I, α W biến điểm M (x; y) thành M’(x’; y’) xác định bởi:    −+−+= −−−+= αα αα ,*MWVMWVN MWV,*MWVN byaxby byaxax  *F,:d%$TVeHeWU Y ZUC,*M α 'CM α f8' Y ZUCM α ['C,*M α C4G#%@(4#%@A>#%)#]-%8*_4#%@AVW,=%$V&1W :g-!6C8VUh&W \ [V'hW \ Zg \ \C4G#%@(4#%@A>#!&%@/8 U \ [' \ h\&Uh\'[,Ze %@*#(=%$V&1W:-!6gZ iC&(4#%9#%9#M*#YY  8 VW8&U['[,Ze V  W8&  U[  '[,  Ze &Z&  HZ  H, ≠ ,  i-:E%<*(/$T:$J%M^ ek ≠ C  $j(/$K% $J%(/$KLM&*,* NOM kOM= uuuuur uuuur (45,#S:E%<%$1%kM^:E%<!C OPQ8 V 1 W 8 N O k V M M→ 1&'8KLZ ( ) ( ) ( ) 1  1 N O k O k V M M V M    ÷   ⇔ = @l$F%9#UT' %%$:E%<,=%S&("8VU e H' e W:(/$KVUH'W%%S&(J ,7&K Y VU Y H' Y W(45,U-,(E/%;,%S&(J,7&:E%<8U Y Z!U[V!WCU e ' Y Z!'[V!WC' e *F,%>%$TVeHeWU Y Z!CU ' Y Z!C' R %:E%<M'@&%kM^:E%<!1:6D8,*K Y ZX VH\W VKWZm!Z\ n- (b#>#%kM^k Vk meW  $j,F(/$K1% ,F(/$KL1LM&*,*KLLZkKC *$J%(/$T,^(E1M^4G#!!"#():#=, α  ( ) oe ee ≤≤ α o 1 (b#>#%$T1%kM^!1#=, α #=, 1 (/$K%K Y M&*,*8 TK Y Z!CTK O6Q8(b#>#pVT1!1 α W VTK1TK Y WZ α V$("#>#T1%kM^(b#>#!1#=,(b#># α W  !Z1(b#># %]&'`VTH α W   α Ze e 1(b#># %:E%<X VTH!W   α Zoe e 1(b#># %:E%<X VTH!W (b#>#,=,-,%6,0%8 &(/$%9##%&(/$%9## V:!"#$%&'()%;%<&(/$(=W1 (4#%9#%(4#%9#1  %&%%&1 (*>%9#%(*>%9#$(J(45,l:dk Vk %k M^,7&(b#>#W1 %&$#-,%%&$#-,(b#>#:d%kM^k1 $J% #=,%#=,,=,B#M^(*1 (4#%@A-!6g%(4#%@A,=- !6g Y Z!CgHT Y ZOCTHVT1T Y WZ α - _E#2&:a&?#&8&#S?#& ,=  '%!&C -,%6,0%,7&:E%<8:E%<%$T%kM^k $J%(b#>#%kM^ l,=,-,%6,0%,7&(b#>#C#*@&1:E%<,=%6,0%(F,Q% M&8(4#%9#^$J%(/$:+,7&=""(]&TH+d’ ,7&(4# %9#d "M*#M*#*F,%@B#:ddC - Kj(b#>#&*#,q#,=%/UI$5%,7&$J%:E%<: $J%C - _E#2&:a&(b#>#8&(45,#S(b#>#:d& ,= (b#># '%!&C RRrs Bài 1. Vn(/$W@*#$F%9#TU',*\(/$tViH\W:RVHuWH(4# %9#8\U[i'huZe &W-,(E+,7&(/$t:(4#%9#]&%E% %I* V\H Wv = − r Vi(W W-,(E(/$KM&*,* V W V B T M = ur C v&W N V W N i \ N \  V A T A x y = = +  ⇔  = − −  ur  ZmtLZVuHiW • *L+,7&]& V T ur HKLVUL1'LW ∈ LHKVU1'W ∈  N V W N \ N \ N  N  V M T M x x x x y y y y = = + = −   ⇔ ⇔   = − = +   ur % :* \VULh\W[iV'L[WuZe \UL[i'LhwZe W  V W \   \ u  V B B B T M x x y y x y = = +  ⇔  = −  = − −  ⇔  = +  ur ZmKViHwW Bài 2.Vn(/$W@*#$F%9#TU',*(4#%9#∆8iUhu'[Ze:(4# %@AVW8VUiW \ [V'[nW \ ZxC-,(E+,7&∆:(4#%@A]&]&'%$ T#=,]&'xe e  +8 &Y* ∆ Y +,7&]& e V 1xe WO Q HKLVUL1'LW ∈ ∆ Y HKVU1'W ∈ ∆ Y &,= N N N N x y y x x y y x = −   =  =  ⇔  = −    :*% ∆ Y 8'LuVULW[Ze uU['[Ze Y$ViHnWH-!6gZi e V 1xe W N V W O I Q I= ZmLZVnHiW g Y ZgZi L8VUhnW \ [V'iW \ Zx Bài 3.Vi(/$W@*#$F%9#TU',*(4#%@AVCW8U \ [' \ hnU[w'ZeC -,(E+,7&(4#%@A]&8 &Y:E%<%$T%kM^!Z\V(W Y(b#>#!%<,Ql% ]&'%$T#=,]&'xe e  :  V 1 iWO V − C + &Y$V\HiW!gZ n V 1\W N V W O H V H= LZVnHwW gLZ\CgZ\ n Xy'VC 1 W8VUnW \ [V'[wW \ Zuw Y e  V 1xe W V W O H Q H=    ViH\W S \ V 1 iW \ V W O H V H − =   \ VxHwW R&! N i CC i nR R= − = Xy'VC 2 W8VU[xW \ [V'[wW \ Z\w . &(/$%9##%&(/$%9## :!"#$%&'()%;%<&(/$( =1  (4#%9#%(4#%9 #1   %&%%& ;1  (*>%9#%(*>%9#?# =1  #=,%#=,?# =1  %&$#-,%%&$#-,?# =1 . (/$K%K Y M&*,*8 TK Y Z!CTK O6Q8(b#>#pVT1 !1 α W VTK1TK Y WZ α V$("#>#T1%kM^(b#># !1 #=,(b#># α W  !Z 1 (b#># %]&'`VTH α W . $j,F(/$K1% ,F(/$KL1LM&*,*KLLZkKC *$J%(/$T,^(E 1 M^4G#!!"#():#=, α  ( ) oe ee ≤≤ α o 1  (b#>#%$T1%kM^ !1 #=, α #=,  1  (/$K%K Y M&*,*8 TK Y Z!CTK O6Q8(b#>#pVT1 !1 α W VTK1TK Y WZ α V$("#>#T1%kM^(b#># !1 #=,(b#># α W 