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Giải bài 2 trang 14 Chuyên đề học tập Toán 11 Chân trời sáng tạo

Cho đường tròn (O) và hai điểm A, B. Khi điểm M thay đổi trên đường tròn (O) thì điểm M’ thay đổi trên đường nào để \(\overrightarrow {MM'} + \overrightarrow {MA} = \overrightarrow {MB} \)?

Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - C𒈔hân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Cho đường tròn (O) và hai điểm A, B. Khi điểm M thay đổi trên đường tròn (O) thì điểm M’ thay đổi trên đường nào để \(\overrightarrow {MM'}  + \overrightarrow {MA}  = \overrightarrow {MB} \)?

Phương pháp giải - Xem chi tiết

Vẽ hình và sử dụng quy tắc hình bình hành để làm

Lời giải chi tiết

Do A, B cố định nên \(\overrightarrow {AB} \) là vectơ không đổi.Từ dữ kiện \(\overrightarrow {MM'}  + \overrightarrow {MA}  = \overrightarrow {MB} \), áp dụng quy tắc hình bình hành, ta có tứ giác ABM’M là hình bình hành.Do đó \(\overrightarrow {MM'}  = \overrightarrow {AB} \)Vì vậy M’ là ảnh của M qua phép tịnh tiến \({T_{\overrightarrow {AB} }}\).Vậy khi M thay đổi trên đường tròn (O) thì M’ nằm trên ảnh của đường tròn (O) là đường tròn (O’) qua phép tịnh tiến \({T_{\overrightarrow {AB} }}\).

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