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Giải bài 5 trang 24 Chuyên đề học tập Toán 11 Chân trời sáng tạo

Trong Hình 12, tìm phép đối xứng biến hình mũi tên (A) thành hình mũi tên (B) và tìm phép đối xứng biến hình mũi tên (B) thành hình mũi tên (C).

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 Hình 12, tìm phép đối xứng biến hình mũi tên (A) thành hình mũi tên (B) và tìm phép đối xứng biến hình mũi tên (B) thành hình mũi tên (C).

Phương pháp giải - Xem chi tiết

Quan sát hình 12 và dựa vào phép đối xứng tâm để làm. Điểm O được gọi là tâm đối xứng của hình H nếu phép đối xứng tâm O biến hình H thành chính nó.

Lời giải chi tiết

⦁ Gọi P, Q là hai điểm nằm trên cạnh của mũi tên (A) như hình vẽ.Lấy O là trung điểm của PQ.

 

Gọi E là một điểm trên hình mũi tên (A).Lấy điểm E’ là ảnh của E quaKhi đó O là trung điểm của EE’, E’ một điểm trên hình mũi tên (B) có vị trí tương ứng với điểm E trên hình mũi tên (A).Tương tự như vậy, với mỗi điểm M bất kì trên hình mũi tên (A), ta lấy điểm M’ là ảnh của M qua  thì ta được tập hợp các điểm M’ tạo thành hình mũi tên (B).Vậy phép đối xứng tâm O biến hình mũi tên (A) thành hình mũi tên (B), với O là trung điểm của PQ trên hình mũi tên (A) (như hình vẽ).⦁ Gọi H, K là hai điểm nằm trên cạnh của mũi tên (B) như hình vẽ.Lấy I là trung điểm của HK.

 

Chứng minh tương tự như trên, ta thu được phép đối xứng tâm I biến hình mũi tên (B) thành hình mũi tên (C), với I là trung điểm của HK trên hình mũi tên (B) (như hình vẽ).

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