Trong mặt phẳng Oxy cho $\Delta ABC$, biết $A(5;2)$. trung trực cạnh BC và trung tuyến CC' lần lượt có phương trình là $x+y-6=0$ và $2x+y-3=0$. tìm tọa độ các đỉnh của $\Lambda ABC$
ptts cua $CC'$:$\left\{ \begin{array}{l} x=t\\ y=3-2t \end{array} \right.$
$C'\in CC'\Rightarrow C'(m;3-2m)$
$C'$ la trung diem cua $AB\Rightarrow B(2m-5;4-4m)$
$C\in CC'\Rightarrow C(n;3-2n)\Rightarrow \overrightarrow{BC}=(n-2m+5;4m-2n-1)$
goi $d$ la duong trung truc cua $BC\Rightarrow \overrightarrow{u}=(1:-1)$ la vecto chi phuong cua $d$
$d $ vuong goc $BC$
$\Rightarrow \overrightarrow{BC}.\overrightarrow{u}=0\Leftrightarrow n-2m+5-4m+2n+1=0\Leftrightarrow n-2m+2=0(1)$
lai co:$d_{(B;d)}=d_{(C;d)}\Leftrightarrow |2m-5+4-4m-6|=|n+3-6|$
hay$|-2m-7|=|-3-n|   (  2)$
Tu $(1),(2)\Rightarrow \left\{ \begin{array}{l} m=\frac{4}{3}\\ n=-6 \end{array} \right.$
Vay $B(-9;12),C(-6;15)$

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