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Giải bài 6 trang 24 Chuyên đề học tập Toán 11 Cánh diều

Trong Hình 40, hình màu xanh là ảnh của hình màu cam qua một phép quay. Xác định tâm và góc quay của phép quay đó.

Tổng h𝔉ợp đề thi học kì 2 lớp 11 tấ꧃t cả các môn - Cánh diều

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

Trong Hình 40, hình màu xanh là ảnh của hình màu♉ cam qua một phép quay. Xác định tâm và góc quay của phép quay đó.

Phương pháp giải - Xem chi tiết

Xác định tâm và góc quay dựa vào định nghĩa:  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

Ta thấy:+)\(CH{\rm{ }} = {\rm{ }}CI,{\rm{ }}CM{\rm{ }} = {\rm{ }}CK,{\rm{ }}CJ{\rm{ }} = {\rm{ }}CL,{\rm{ }}CN{\rm{ }} = {\rm{ }}CO,{\rm{ }}CE{\rm{ }} = {\rm{ }}CG,{\rm{ }}CD{\rm{ }} = {\rm{ }}CF\;\) (đường chéo của các hình chữ nhật có cùng kích thước).+) \(\widehat {HCI} = \widehat {MCK} = \widehat {JCL} = \widehat {NCO} = \widehat {ECG} = \widehat {DCF} = 90^\circ \).Do đó, ta có phép quay tâm C, góc quay 90° biến các điểm H, M, J, N, E, D tương ứng thành các điểm I, K, L, O, G, F.Như vậy, hình màu xanh là ảnh của hình màu cam quay phép quay tâm C, góc quay 90°.

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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