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Giải bài 4 trang 29 Chuyên đề học tập Toán 11 Chân trời sáng tạo

Chỉ ra phép quay có thể biến mỗi hình trong Hình 10 thành chính nó.

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

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Đề bài

Chỉ ra phép quay có thể biến mỗi hình trong Hình 10 thành chính nó.

Phương pháp giải - Xem chi tiết

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

⦁ Hình 10a:Hình vẽ có dạng hình vuông, gọi O là tâm hình vuông đó và A là 1 đỉnh của hình vuông.Phép quay tâm O, góc quay 180° biến điểm A thành điểm A’.Tương tự, ta chọn các điểm khác bất kì trên Hình 10a.Khi đó qua phép quay tâm O, góc quay 180° ta cũng xác định được ảnh của các điểm đó trên Hình 10a ban đầu.Vậy phép quay biến Hình 10a thành chính nó là phép quay tâm O, góc quay 180°.

Ngoài ra, phép quay tâm O, góc quay –180° cũng biến Hình 10a thành chính nó.

⦁ Hình 10b:Hình vẽ có dạng hình vuông, gọi I là tâm hình vuông đó và B là 1 đỉnh của hình vuông.Phép quay tâm I, góc quay 90° biến điểm B thành điểm B’.Tương tự, ta chọn các điểm khác bất kì trên hình 10b.Khi đó qua phép quay tâm I, góc quay 90° ta cũng xác định được ảnh của các điểm đó trên Hình 10b ban đầu.Vậy phép quay biến Hình 10b thành chính nó là phép quay tâm I, góc quay 90°.

Chú ý: Có nhiều phép quay biến Hình 10a thành chính nó, chẳng hạn ngoài phép quay ở trên, ta có thể kể đến phép quay tâm I, góc quay 180° hoặc phép quay tâm I, góc quay –90°, …

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