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Giải bài 33 trang 81 SBT toán 10 - Cánh diều

Phương trình nào dưới đây là phương trình tham số của một đường thẳng song song với đường thẳng x − 2y + 3 = 0?

🐟Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Cánh diều

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Phương trình nào dưới đây là phương trình tham số của một đường thẳng song song với đường thẳng

x − 2y + 3 = 0?

A. \(\left\{ \begin{array}{l}x =  - 1 + 2t\\y = 1 + t\end{array} \right.\)            B. \(\left\{ \begin{array}{l}x = 1 + 2t\\y =  - 1 + t\end{array} \right.\)                       C. \(\left\{ \begin{array}{l}x = 1 + t\\y =  - 1 - 2t\end{array} \right.\)          ಌD. \(\left\{ \begin{array}{l}x = 1 - 2t\\y =  - 1 + t\end{array} \right.\)

Phương pháp giải - Xem chi tiết

Bước 1: Tìm các đường thẳng có VTCP nhân vô hướng với VTPT của đường thẳng x − 2y + 3 = 0 bằng 0

Bước 2: Lấy 1 điểm trên các đường thẳng đã tìm ở bước 1, thay tọa độ điểm đó vào PT đường thẳng

x − 2y + 3 = 0. Nếu điểm đó không thuộc đường thẳng x − 2y🌺 + 3 = 0 thì đường thẳng chứa điểm đó là đường thẳng cần tìm

Lời giải chi tiết

Đường thẳng ∆: x − 2y🧸 + 3 = 0 có VTPT là \(\overrightarrow n  = (1; - 2)\).

Đường thẳng dꦫ song song với ∆ nhận \(\overrightarrow n  = (1; - 2)\) làm VTPT và có VTCP là \(\overrightarrow u \) thỏa mãn \(\overrightarrow u .\overrightarrow n  = 0\)

 (Loại C, D)

Xét điểm M(-1; 1) thuộc đường thẳng \(\left\{ \begin{array}{l}x =  - 1 + 2t\\y = 1 + t\end{array} \right.\). Ta thấy tọa độ M thỏa mãn PT x − 2y + 3 = 0 nên M nằm trên ∆ (Loại A)

 Chọn B

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