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Giải bài 48 trang 99 SBT toán 10 - Cánh diều

Cho tam giác ABC và M là trung điểm của BC, G là trọng tâm của tam giác. Khẳng định nào sau đây đúng?

💫Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Cánh diều

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Cho tam giác ABC và M là trung điểm của BC, G là trọng tâm của tam giác. Khẳng định nào sau đây đúng?

A. \(\overrightarrow {AM}  =  - 3\overrightarrow {GM} \)          B. \(\overrightarrow {AM}  = \frac{3}{2}\overrightarrow {GM} \)            C. \(\overrightarrow {AM}  =  - \frac{3}{2}\overrightarrow {GM} \)          D. \(\overrightarrow {AM}  = 3\overrightarrow {GM} \)

Phương pháp giải - Xem chi tiết

Sử dụng tính chất đường trung tuyến trong tam giác và xác định hướng các vectơ tương ứng

Lời giải chi tiết

∆ABC có AM là đường trung tuyến và G là trọng tâm nên \(AG = \frac{2}{3}AM\) \( \Rightarrow AM = 3GM\)

Lại có G nằm giữa A và M \( \Rightarrow \overrightarrow {AM}  = 3\overrightarrow {GM} \)  

 Chọn D

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Ph/hs Tham Gia Nhóm Để Cập Nhật Điểm Thi, Điểm Chuẩn Miễn Phí

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