BÀI TẬP PHƯƠNG PHÁP TỌA ĐỘ TRONG MẶT PHẲNG Bài 1 !"#$ %& !'#$(%& )*+, "/$0123 4,1 Giải 56),4,7684,56)94,9 "$ " $ & "$ $: ; / ' $( & $: ; ; ; x x y B x y y  =  − + =     ⇔ ⇒    ÷ − + =     =   <)=)2568),76>?),76@A)9+ .$/ "0/ .$/ '0/ . / 0 AB BD AC n n n a b− − uuur uuur uuur .với a 2 + b 2 > 005B5C56DE4,2 1F) , ( ) ( ) G  G  AB BD AC AB c n n c n n= uuur uuur uuur uuur " " " " : " ' H & " ' a b a b a b a ab b b a = −   ⇔ − = + ⇔ + + = ⇔  = −  IDJ),%I>1K,%$ ⇒ >%I$1F)E!!$%& %∩8)L56)94,9 $ & : .:/"0 " $ & " x y x A x y y − − = =   ⇒ ⇒   − + = =   MK)N56ON%∩8N56)94,9 ' $ & ' ; " / ' $( & ; " " " x x y I x y y  =  − − =     ⇔ ⇒    ÷ − + =     =   N56+)L4,768 ( ) $( $" (/: / / ; ; C D    ÷   IDJ)>%I',.5)7@PQ0 Bài 27J)9 R.0 " "   " H H & + + − − = 1D)S  GG7J) T:#I"%&76Q RUTO+T6) >?V1 "1>,)L.$/;/(0.&/$/$0.$/"/$01K,)L+ G,T6) WX1 Giải Y R.0ON.I$/(0>2@AZ%; MK) B56∆ %[∆:##%&\".7]]7J) :#I"%&0 D Q RUTO+T6)>?V%[@^2_ONS∆>? " " ; : (− = ( ) " ( $& $ : (  ( : $ ( $& $ c c d I c  = − − + + ⇒ ∆ = = ⇔  + = − −   .W,`\"0 D RB56 : ( $& $ &x y + + − =  : ( $& $ &x y + − − = 1 Bài 3: D)S24,,)2>)S."/I$0 ,76 O)2*+, 35B5C56.T $ 0:!(#"'%&76.T " 0#"!;%& Giải PT c¹nh BC ®i qua B(2 ; -1) vµ nhËn VTCP ( ) $ + (/:= uur cña (d 2 ) lµm VTPT (BC) : 4( x- 2) + 3( y +1) = 0 hay 4x + 3y - 5 =0 +) Täa ®é ®iÓm C lµ nghiÖm cña HPT : ( ) ( : ; &  $  $/:  " ; &  : + − = = −   ⇔ ⇒ = −   + − = =   +) §êng th¼ng ∆ ®i qua B vµ vu«ng gãc víi (d 2 ) cã VTPT lµ ( ) " + "/ $ = − uur ∆ cã PT : 2( x - 2) - ( y + 1) = 0 hay 2x - y - 5 = 0 +) Täa ®é giao ®iÓm H cña ∆ vµ (d 2 ) lµ nghiÖm cña HPT : ( ) "  ; &  : a :/$  " ; &  $ − − = =   ⇔ ⇒ =   + − = =   +) Gäi B’ lµ ®iÓm ®èi xøng víi B qua (d 2 ) th× B’ thuéc AC vµ H lµ trung ®iÓm cña BB’ nªn : ( ) b a  b a   "  ( b (/:  "  : = − =  ⇒ =  = − =  +) §êng th¼ng AC ®i qua C( -1 ; 3) vµ B’(4 ; 3) nªn cã PT : y - 3 = 0 +) Täa ®é ®iÓm A lµ nghiÖm cña HPT :  : &  ;  . ;/:0 : ( "' &  : − = = −   ⇔ ⇒ = −   − + = =   +) §êng th¼ng qua AB cã VTCP ( )  '/ (= − uuur , nªn cã PT :  "  $ ( ' $ & ' ( − + = ⇔ + − = − B i 4 : à 7J)9K,1 R.0 &$"( "" =−−−+ yxyx 76 T &$ =++ yx 1)L-+ TG,_)L-@c C S.0,))S+SC7J),+d& & #.0ON."$076>2@AZ% V  # BABMA .d& e & = 562)S)L0G+, $""1"1 === RMAMI D-+ RON>2@AZ ] % $" 76-+T8 0K,W,9  ( ) ( )      +−= −= ∨      −−= = ↔      =++ =−+− "$ " "$ " &$ $"$" "" y x y x yx yx D")LW,8+B+>6)2K,8+81 ,1.f0O 0"&$. −J >2@AZ%: #,7 0""$. − → u .E07+P7J),8.E0 → u 567 E.E0T &"" =+−+ Dzyx #.E0Q.f0U R>@%"8T.g.E00% ; "" =−rR 8, ; : 0"1."&1"$ = +−−+ D       −−= +−= ↔ ;:; ;:; D D Giải F<".E $ 0 &;:;"" =+−−+ zyx 76.E " 0 &;:;"" =−−−+ zyx 6); K,)L.$/$076  ∆ "#:#(%&1 K,)L+  ∆ G, 76 ∆ C7J),+(; & M)^) h ∆ ,Gi $ : " " x t y t = −   = − +  767 . :/"0u = − ur h+ ∆  .$ : / " " 0A t t⇒ − − +  h,./ ∆ 0%(; &  $ G. / 0 " c AB u⇔ = uuuur ur  1 $ " 1 AB u AB u ⇔ = uuuur ur ur  " $; : $Vd $;V (; & $: $: t t t t⇔ − − = ⇔ = ∨ = − h2)LB56 $ " :" ( "" :" . / 0 . / 0 $: $: $: $: A A− − Bài 6: 7J)9jOxy ,)  &;" $ =+− yxd 1T " :#V! 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"/$0 " : ' & x y A x y + − =  ⇒ −  − + =  K,356)94,9 ( " & .V/ $0 " : d & x y B x y + − =  ⇒ −  + − =  Y *+,767+P7J) ,@c_856:.!V0#".#$0%& ⇔:#"!$V%&1 +)L+ ++S@c_8K,)L56)99 : " $V & ."/;0 " $ " : d & " " x y C x y + − =   ⇒  − + + − =   1 FS5+.I"/$0.V/I$0."/;01 Bài 9 : 7J)9K, R.0.I(0 " # " %(76)Lr.(/$01K, )L-8j+G,_-@cC,))S+S--S R.07J)562)S )LG, )*+,)Lr Giải : MK)N56O R.0G+,N.(/&01st &/,0+j+6_@cC,))S+S- -S R.01M)^Gu . $ / $ 0/. " / " 01, ( ) / $$ ayxMA −=  ( ) $$ /( yxIA −= 1 D MAIA ⊥ 8 ( ) ( ) ( ) ( ) 1&(((&( $$ " $ " $$$$$ =−−++−⇔=−+− ayxyxayyxx D+.08 1&$"( $$ =−− ayx f+,+  (!,!$"%&1 v+ (!,!$"%&1 56(!,!$"%&1 Y )*+,r.(/$08,%(1 Y)LB56 &/(01 2@2)S+S). $ / $ 0T ( ) 1 1 4 ( 4) 4 0x x y y- - + - = D)S+S*+, &/,08 ( ) 1 1 4 ( 4) 4 0x ya- - + - = vK,. " / " 0W, ( ) 2 2 4 ( 4) 4 0x y a- - + - = f+,56(!,!$"%&1 Bài 10 : 7J)9K, R.0 $ "" =+ yx 12)2nv4,L 8 %l)w")L6_x))LL@cC,))S+S7J).0G, ),,))S+S>?V&  1 Giải : Y RO.&/&076>2@AZ%$1 M)^GuEE56,))S+S.562)S)L01 • kS+ POPBPA o ⇒=⇒= "V& e + R. $ 0O>2@AZ%"1 • kS+ POPBPA o ⇒=⇒= : " $"& e + R. " 0O>2@AZ% : " 1 Y %W,`8+B+>6)2Q R. $ 076@P)L+7J) R . " 01 • Y %Q. $ 0 "" <<−⇔ m 1 • Y %@P)L+7J) . " 0 : " −<⇔ m  1 : " >m f+,2)2nB4,56 1" : " : " " <<−<<− mvam  Bài : 7J)9K,>,  T $ "#!:%&T " #"!(%&76T : "!!"%&1 D)S RO+T $ 76)Swl )7J)T " T : 1 Giải : MK)N56O76@A)9+Z56>2@A4, R1 D $ I d ∈ 8K,4,NTN%./:!"01 Y R.N0)Sw7J)T " 76T : @)763@) T.N/T " 0%T.N/T : 01.h0 , ( ) ( ) ( ) " : " ( " : " " h ; ; t t t t + − − − − − ⇔ =  : : " ( ; $ t t t t =  ⇔ − = − ⇔  =  I DJ)%:,N%.:I:076 ' ; R = / I DJ)%$,N%.$/$076 $ ; R = 1 D,) RW,`8+B+>6)2/4,w56 ( ) ( ) ( ) ( ) " " " " (d $ : : 6 I$ $ ; ; x y v y− + + = + − = Bài 11: 7J)9K, .I$0 " #.#:0 " %d76 T !#$%&185X)L-768T5X)LkG,iK,56+)L4,-k1K, 4,2)L-76k Giải : D N d ∈ 8K,4,kTk%./#$01 D-76ki)=7J),+*+,8-%.I/II$01 D M C ∈ 8 ( ) ( ) ( ) " " $ $ : d1 ht t − − + − − + = , ( ) " h " & $ "1 ⇔ − − = ⇔ = − = t t t hay t I DJ)%I$,-%.$/&076k%.I$/&01 DJ)%",-%.I"/I:076k%."/:01 Bi 12 : 7J)9K,,) T $ #!"%&76 T " "!#:%&18T $ 5X)L-768T " 5X)LkG, " &OM ON + = uuuur uuur r 1K,4, )L-76k1 Gii : D $ M d 8K,4,-T-%.,/"!,01 D " N d 84,kTk%.>/">#:01 , ( ) " & " & " & " " " : & ( H a b a b OM ON a b a b + = + = + = + + = = uuuur uuur r H ( 1 : : a b = = D H " ( $ / 6 k% I / 1 : : : : M v = ữ ữ Bi 13: 7J)9K,,)27J) ; . $/ $0AB C = #"!:%&76KO4,,)2+ #!"%&1a`K, 23761 Gii : MK)N./056+)L4,76M. M / M 056KO4,1 " : CG CI = 8 " $ " $ / 1 : : G G x y x y = = f+,K,)LNW,`9 " : & .;/ $0 " $ " $ " & : : x y I x y + = + = 1 ; " " AB IA IB = = = 8K,2)L56,))9@2,+4,9 " " " : & ( ; $ . ;0 . $0 ( " x y x x y y + = = + + = = V : 1 " x y = = 1K,4,2)L56 $ : (/ V/ 1 " " ữ ữ Bi 14 : Trong mặt phẳng Oxy cho tam giác ABC biết A(2; - 3), B(3; - 2), có diện tích bằng : " và trọng tâm thuộc đờng thẳng : 3x y 8 = 0. Tìm tọa độ đỉnh C Gii Ta có: AB = " , trung điểm M ( ; ; / " " ), pt (AB): x y 5 = 0. S ABC = $ " d(C, AB).AB = : " d(C, AB)= : " Gọi G(t;3t-8) là trọng tâm tam giác ABC thì d(G, AB)= $ " d(G, AB)= .: H0 ; " t t = $ " t = 1 hoặc t = 2 G(1; - 5) hoặc G(2; - 2) Mà :CM GM= uuuur uuuur C = (-2; -10) hoặc C = (1; -1) Bài 15 :  R.0x 2 + y 2 = 1;76x 2 + y 2 – 2(m + 1)x + 4my – 5 = 0 (1)=)?.$0564, R7J)K)1MK)2  R=56.  01L.  0)Sw7J).01 Giải: .0O.&/&0>2@AZ%$.  0OI.#$/I"0>2@A " " b . $0 ( ;R m m= + + + N " " . $0 (m m= + + ,NyZm  D.076.  03)S+1%%[Zm!Z%N.7Zm[Z0 M)^),%I$/%:]; Bài 16 :K,.0,)2KOM $$ $/ :    ÷     +v4, − :#H%&76  (#!d%&1s2nK,234,,)21 Giải ,+ 8.,/d!(,0.>/d!(>0 M.$/ $$ 0 : 56KO,)28.I,I>#:/(,#(>!'0 TI:#H%&DE56 .:/$0u r / MK)N56+)L,N : /" $ " a a −   +  ÷   1T56+v4, ⇔  1 & I d BC u ∈    =   uuur r ( ) : :." $0 H & " :1 : " .( H $V0 & a a b a a b −  − + + =  ⇔   − − + + − =  $ : a b =  ⇔  =   D.$/;0.:/I:076.I$/d0 . BÀI TẬP PHƯƠNG PHÁP TỌA ĐỘ TRONG MẶT PHẲNG Bài 1. ữ ữ Bi 14 : Trong mặt phẳng Oxy cho tam giác ABC biết A(2; - 3), B(3; - 2), có diện tích bằng : " và trọng tâm thuộc đờng thẳng : 3x y 8 = 0. Tìm tọa độ đỉnh C Gii Ta có:. −   .W,`"0 D RB56 : ( $& $ &x y + + − =  : ( $& $ &x y + − − = 1 Bài 3: D)S24,,)2>)S."/I$0 ,76 O)2*+, 35B5C56.T $ 0:!(#"'%&76.T " 0#"!;%& Giải PT