Cho tam giác ABC có A(2,3); B(-3;4); C(1,1) xác định tọa độ trọng tâm G và trực tâm H của tam giác ABC
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NV
Nguyễn Việt Lâm
Giáo viên
15 tháng 2 2022
Áp dụng công thức trọng tâm:
\(\left\{{}\begin{matrix}x_C=3x_G-x_A-x_B=-3\\y_C=3y_G-y_A-y_B=-4\end{matrix}\right.\) \(\Rightarrow C\left(-3;-4\right)\)
\(\Rightarrow\overrightarrow{CA}=\left(4;5\right)\) ; \(\overrightarrow{AB}=\left(1;2\right)\)
Đường cao d đi qua B vuông góc AC nên nhận \(\overrightarrow{CA}=\left(4;5\right)\) là 1 vtpt
Phương trình d:
\(4\left(x-2\right)+5\left(y-3\right)=0\Leftrightarrow4x+5y-23=0\)
Đường cao d1 đi qua C vuông góc AB nên nhận (1;2) là 1 vtpt
Phương trình d1:
\(1\left(x+3\right)+2\left(y+4\right)=0\Leftrightarrow x+2y+11=0\)
H là giao điểm d và d1 nên tọa độ thỏa mãn:
\(\left\{{}\begin{matrix}4x+5y-23=0\\x+2y+11=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{101}{3}\\y=-\dfrac{67}{3}\end{matrix}\right.\) \(\Rightarrow H\left(\dfrac{101}{3};-\dfrac{67}{3}\right)\)
18 tháng 12 2021
\(\left\{{}\begin{matrix}x_G=\dfrac{-1+\left(-2\right)+4}{3}=\dfrac{1}{3}\\y_G=\dfrac{1+3+\left(-5\right)}{3}=-\dfrac{1}{3}\end{matrix}\right.\)
15 tháng 6 2022
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