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Giải bài 4.25 trang 58 sách bài tập toán 10 - Kết nối tri thức với cuộc sống

Trong mặt phẳng tọa độ Oxy cho hai điểm M( - 3;2) và N(2;7). a) Tìm tọa độ của điểm P thuộc trục tung sao cho M,N,P thẳng hàng. b) Tìm tọa độ của điểm Q đối xứng với N qua Oy. c) Tìm tọa độ của điểm R đối xứng với M qua trục hoành.

ღTổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Kết nối tri thức

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

Trong mặt phẳng tọa độ \(Oxy\) cho hai điểm \(M( - 3;2)\) và \(N(2;7).\) a) Tìm tọa độ của điểm \(P\) thuộc trục tung sao cho \(M,\,\,N,\,\,P\) thẳng hàng. b) Tìm tọa độ của điểm \(Q\) đối xứng với \(N\) qua \(Oy.\) c) Tìm tọa độ của điểm \(R\) đối xứng với \(M\) qua trục hoành.

Lời giải chi tiết

a) Vì \(P\) thuộc trục tung nên tọa độ điểm \(P\) là \(P(0;y)\)Ta có: \(\overrightarrow {MN}  = (5;5)\), \(\overrightarrow {MP}  = (3;y - 2)\)Để ba điểm \(M,\,\,N,\,\,P\) thẳng hàng\( \Leftrightarrow \) hai vectơ \(\overrightarrow {MN} \) và \(\overrightarrow {MP} \) cùng phương\( \Leftrightarrow \) \(5\left( {y - 2} \right) - 5.3 = 0\)\( \Leftrightarrow \) \(5y - 10 - 15 = 0\)\( \Leftrightarrow \) \(5y = 25\)\( \Leftrightarrow \) \(y = 5\)Vậy \(P(0;5).\)b) Tọa độ điểm \(Q\) đối xứng với \(N\) qua \(Oy\) là: \(Q( - 2;7).\)c) Tọa độ của điểm \(R\) đối xứng với \(M\) qua trục hoành là: \(R( - 3; - 2).\)

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Ph/hs Tham Gia Nhóm Để Cập Nhật Điểm Thi, Điểm Chuẩn Miễn Phí

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