hình học phẳng ngắn mà hay !!

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r0cket95

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teenboya8

r0cket95 said:
câu 1: cho tam giac ABC có S=2, AB : x-y=0 . I (2;1) là trung điểm BC . Tìm tọa độ trung điểm K của AC ?

câu 2: cho tam giac ABC cân tại A , AB : x - y +6 =0 , BC : x+2y=0 . viết phương trình đường cao kẻ từ B ?
Bấm để xem đầy đủ nội dung ...
Chào bạn!
Mình thấy khi vẽ hình bài 2 thì ta tìm được vô số tam giác cân tại A thỏa mãn điều kiện.
Ta có điểm B là giao của hai đường thẳng.
Cứ mỗi điểm A trên AB thì tương ứng có 1 điểm C trên BC.
Bạn xem lại đề nhé!
 
R

rocky576

r0cket95 said:
câu 1: cho tam giac ABC có S=2, AB : x-y=0 . I (2;1) là trung điểm BC . Tìm tọa độ trung điểm K của AC ?
Bấm để xem đầy đủ nội dung ...
Ta có: IK là đường trung bình của tam giác ABC nên đường thẳng IK có VTPT là:
\[\overrightarrow n {}_{IK} = \overrightarrow n {}_{AB} = (1; - 1)\]
và IK qua I(2;1) $\Rightarrow $pt đường thẳng IK là:
\[(IK):x - y - 1 = 0\]
\[\begin{array}{l}
B(b;b);A(a;a);C({c_1};{c_2})\\
\left\{ \begin{array}{l}
b + {c_1} = 4\\
b + {c_2} = 2
\end{array} \right. \Rightarrow {c_1} - c{}_2 = 2 \Rightarrow {c_1} = c{}_2 + 2\\
\overrightarrow {AI} = (2 - a;1 - a) \Rightarrow {\overrightarrow n _{AI}} = (1 - a;a - 2) \Rightarrow (AI):(1 - a)(x - 2) + (a - 2)(y - 1) = 0\\
\overrightarrow {AC} = (c{}_2 + 2 - a;{c_2}) \Rightarrow {\overrightarrow n _{AC}} = ({c_2};a - {c_2} - 2) \Rightarrow (AC):{c_2}(x - c{}_2 - 2) + (a - {c_2} - 2)(y - {c_2}) = 0\\
\Rightarrow \alpha \left[ {(1 - a)(x - 2) + (a - 2)(y - 1)} \right] + \beta \left[ {{c_2}(x - c{}_2 - 2) + (a - {c_2} - 2)(y - {c_2})} \right] = x - y
\end{array}\]

......................................
thôi mình chịu thua, bạn xem lại cái đề nhé, cho thêm 1 ít dữ kiện đi bạn ơi
 
D

dothanhdat2526

r0cket95 said:
câu 1: cho tam giac ABC có S=2, AB : x-y=0 . I (2;1) là trung điểm BC . Tìm tọa độ trung điểm K của AC ?
Bấm để xem đầy đủ nội dung ...
mình nói qua cách giải thôi nhé : IK là đường TB nên IK//AB -->lập ptr đt IK .
S= 1/2.d(I,AB).AB=1----> AB ----> IK=AB/2 ---> K . ;);)
 
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