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Giải bài 36 trang 81 SBT toán 10 - Cánh diều

Đường thẳng ∆ đi qua điểm M(3 ; -4) và vuông góc với đường thẳng d: x − 3y + 1 = 0 có phương trình tổng quát là:

♏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

Đường thẳng ∆ đi qua điểm M(3 ; -4) và vuông góc với đường thẳng  d: x − 3y + 1 = 0 có phương trình tổng quát là:

A. x - 3y – 15 = 0        B. -3x + y + 5 = 0        C. 3x + y – 13 = 0       D.  3x + y – 5 = 0

Phương pháp giải - Xem chi tiết

Bước 1: Tìm một VTPT của ∆ (thỏa mãn nhân vô hướng với VTPT của d bằng 0)

Bước 2: Viết PTTQ của ∆ biết điểm đi qua là M và VTPT đã tìm ở bước 1

Lời giải chi tiết

d꧙ có VTPT \(\overrightarrow n  = (1; - 3)\) \( \Rightarrow d\) có VTCP là \(\overrightarrow u  = (3;1)\)

Do ∆ \( \bot \) d nên ∆ nhận \(\overrightarrow u  = (3;1)\) làm VTPT.

∆ có PT: 3x + y – 5 = 0    

Chọn D

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