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Giải bài 11 trang 25 Chuyên đề học tập Toán 11 Cánh diều

Hình 44 mô tả một viên gạch trang trí hình tam giác đều. Xác định phép quay biến:

🐎Tổng hợp đề thi học kì 2 lớp 11 tất c🐻ả các môn - Cánh diều

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

Hình 44 mô tả một viê꧒n gạch tra▨ng trí hình tam giác đều. Xác định phép quay biến:

a) Cánh hoa màu xanh đỉnh A thành cánh hoa màu xanh đỉnh B. b) Cánh hoa màu đỏ đỉnh E thành cánh hoa màu đỏ đỉnh D.

Phương pháp giải - Xem chi tiết

Xác định tâm và góc quay: Trong mặt phẳng, cho điểm O cố định và góc lượng giác \(\varphi \) không đổi. Phép biến hình biến điểm O thành điểm O và biến mỗi điểm M khác O thành M’ sao cho \(OM = OM'\) và góc lượng giác \(\left( {OM,OM'} \right) = \varphi \) được gọi là phép quay tâm O với góc quay \(\varphi \), kí hiệu \({Q_{\left( {O,\varphi } \right)}}\). O gọi là tâm quay, \(\varphi \) gọi là góc quay.

Lời giải chi tiết

a) Đặt điểm O là tâm của các cánh hoa như hình vẽ. Do tam giác ABC là tam giác đều nên OA = OB và \(\widehat {AOB} = 120^\circ \). Do đó, ta có phép quay tâm O với góc quay 120° biến điểm O thành điểm O và điểm A thành điểm B. Như vậy, phép quay tâm O với góc quay 120° biến cánh hoa màu xanh đỉnh A thành cánh hoa màu xanh đỉnh B.b) Ta cũng có OE = OD và \(\widehat {EOD} = 120^\circ \) nên ta có phép quay tâm O với góc quay – 120° biến điểm O thành điểm O, biến điểm E thành điểm D. Như vậy, phép quay tâm O với góc quay – 120° biến cánh hoa màu đỏ đỉnh E thành cánh hoa màu đỏ đỉnh D.

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