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Giải bài 8 trang 41 Chuyên đề học tập Toán 11 Chân trời sáng tạo

Trong mặt phẳng tọa độ Oxy, cho điểm M(–2; 4). Phép vị tự tâm O tỉ số \(k = -2\) biến điểm M thành điểm nào trong các điểm sau?

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

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

Trong mặt phẳng tọa độ Oxy, cho điểm M(–2; 4). Phép vị tự tâm O tỉ số \(k = -2\)  biến điểm M thành điểm nào trong các điểm sau? A. (–3; 4). B. (–4; –8). C. (4; –8). D. (4; 8).

Phương pháp giải - Xem chi tiết

Nếu \({V_{(I,k)}}{\rm{[}}M(x,y){\rm{]}} = M'(x',y')\). Khi đó, \(\left\{ \begin{array}{l}x' - a = k(x - a)\\y' - b = k(y - b)\end{array} \right.\) với \(I(a;b)\)

Lời giải chi tiết

Đáp án đúng là: C

Ta đặt M’(x’; y’) là ảnh của điểm M qua phép vị tự tâm O tỉ số \(k{\rm{ }} = {\rm{ }}-2.\)Suy ra \(\overrightarrow {OM'}  =  - 2\overrightarrow {OM} \)Do đó \(\left\{ \begin{array}{l}x' - 0 =  - 2.( - 2 - 0)\\y' - 0 =  - 2.(4 - 0)\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}x' = 4\\y' =  - 8\end{array} \right.\)Vậy tọa độ M’(4; –8) thỏa mãn yêu cầu bài toán.Do đó ta chọn phương án C.

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