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Giải bài 6 trang 33 Chuyên đề học tập Toán 11 Cánh diều

Chứng minh rằng qua phép vị tự tâm O tỉ số k (k ≠ 0), ảnh của mọi đường thẳng đi qua tâm O là chính nó.

Tổng hợp đề thi học kì 2 lớp 11 tất cả cá🦋c môn - Cánಌh diều

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Đề bài

Chứng minh rằng qua phép vị tự tâm O tỉ số k (k ≠ 0), ảnh của mọi đường thẳng đi qua tâm O là chính nó.

Phương pháp giải - Xem chi tiết

Nếu phép vị tự tâm O tỉ số k \(\left♚( {k \ne 0} \right)\) lần lượt biến 2 điểm A, B thành 2 điểm A’, B’ thì \(A'B' = \left| k \right|AB\)

Lời giải chi tiết

Theo định lí về tính chấtꦦ của phép vị tự ta có: Phép vị tự tâm O tỉ số k (k ≠ 0) biến đường thẳng thành đường thẳng song song hoặc trùng v♏ới nó.

Giả sử qua phép vị tự tâm O tỉ số k (k ≠ 0) biến đường thẳng d thành đường thẳ🅺ng d' thì d // d' hoặc d ≡ d'.

Mà O cố định, O thuộc đường thẳng d (gi🧸ả thiết) và phép vi tự tâm O tỉ số k (k ≠ 0) biến điểm O thành chính nó nên O cũng thuộc đường thẳng d'. Do đó, d và d' không thể song song với nhau nên d và d' trùng nhau.

Như𒅌 vậy, phép vị tự tâm O tỉ số k (k ≠ 0) biến đường thẳng d t𝕴hành đường thẳng trùng với chính nó. 

Nói cách khác: Qua phép 🌳vị tự tâm O tỉ số🏅 k (k ≠ 0), ảnh của mọi đường thẳng đi qua tâm O là chính nó. 

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