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Giải bài 4.1 trang 47 sách bài tập toán 10 - Kết nối tri thức với cuộc sống

Cho tam giác \(ABC\). Gọi \(M\) là trung điểm của cạnh \(BC\) và \(G\) là trọng tâm của tam giác. Trong các khẳng định sau, khẳng định nào là một khẳng định đúng?

♓Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Kết nối tri thức

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

Cho tam giác \(ABC\). Gọi \(M\) là trung điểm của cạnh \(BC\) và \(G\) là trọng tâm của tam giác. Trong các khẳng định sau, khẳng định nào là một khẳng định đúng? a)      Hai vectơ \(\overrightarrow {GA} \) và \(\overrightarrow {GM} \) cùng phương. b)     Hai vectơ \(\overrightarrow {GA} \) và \(\overrightarrow {GM} \) cùng hướng. c)      Hai vectơ \(\overrightarrow {GA} \) và \(\overrightarrow {GM} \) ngược hướng. d)     Độ dài của vectơ \(\overrightarrow {AM} \) bằng ba lần độ dài của vectơ \(\overrightarrow {MG} \).

Phương pháp giải - Xem chi tiết

-  Sử dụng tính chất của trọng tâm tam giác -  Các định các vectơ cùng phương, cùng hướng hay ngược hướng.

Lời giải chi tiết

Xét \(\Delta ABC\) có: \(M\) là trung điểm của \(BC\)\(G\) là trọng tâm của \(\Delta ABC\)\( \Rightarrow \,\,AG = \frac{2}{3}GM.\)mặt khác \(\overrightarrow {GA} \) và \(\overrightarrow {GM} \) ngược hướngnên \(\left| {\overrightarrow {AM} } \right| = 3\left| {\overrightarrow {MG} } \right|\)Vậy khẳng định a,c,d là khẳng định đúng còn khẳng định b là khẳng định sai.

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

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