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Giải bài 3 trang 20 SGK Toán 10 tập 2 – Cánh diều

Trong mặt phẳng, cho hai đường thẳng song song a và b. Cho 3 điểm phân biệt trên đường thẳng a và 4 điểm phân biệt trên đường thẳng b. Có bao nhiêu tam giác có cả 3 đỉnh là 3 điểm trong 7 điểm nói trên?

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

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

Trong mặt phẳng, cho hai đường thẳng song song a và b. Cho 3 điểm phân biệt trên đường thẳng a và 4 điểm phân biệt trên đường thẳng b. Có bao nhiêu tam giác có cả 3 đỉnh l🎃à 3 điểm trong 7 điểm nói trên?

Phương pháp giải - Xem chi tiết

Một tam giác được tạo nên bởi 3 điểm không thẳng hàng, do đó để có một tam giác ta sẽ chọn ra 3 điểm không 👍thằng hàng�� trong 7 điểm đã cho.

Cách 1:

Lấy 2 điểm thuộc a, 1 điểm thuộc b và ngược lại.

Cách 2:

Tính số cách chọn 3 điểm bất ꦐkì trong 7 điểm – số cách chọn 3 điểm th✨ẳng hàng thuộc a và b.

Lời giải chi tiết

Cách 1:

TH1: 2 điểm thuộc a và 1 điểm thuộc b

Số cách chọn 2 điểm thuộc đườn🦩g thẳng a là \(C_3^2\) (cách chọn)

Số cách chọn 1 đi𒐪ểm thuộc đường thẳng b là: \(C_4^1\) (cách ♛chọn)

=&g🅠t; Số tam giác tạo thành là: \(C_3^2 . C_4^1 = 12\)

TH2: 2 điểm thuộc b và 1 điểm thuộc a

Số cách chọn 2 điểm thuộc đường thẳng b là \(C_4^2ও\) (cách chọn)

Số cách chọn 1 điểm thuộc đường ᩚᩚᩚᩚᩚᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ𒀱ᩚᩚᩚthẳng a là: \(C_3^1\) (cách chọn)

=> Số tam giác tạo th🌊ành là: \(C_4🐻^2 . C_3^1 = 18\)

Vậy có tất cả 12 + 18 = 30 tam giác.

Cách 2:

Số c𝓡ách chọn 3 điểm thuộc đường thẳng a l🌠à: \(C_3^3\) (cách chọn)

Số cách cꦕhọn 3 điểm thuộc đường thẳng b là: \(C_4^3\) (cách ch🐲ọn)

Số cách c✨họn 3 điểm bất kì trong 7 điểm đã cho là: \(C_7^3\) (cách chọn)

Số cách chọnꦯ 3 điểm không thẳng hàng trong 7 điểm đã cho là: \(C_7^3 - C_4^3 - C_3^3🥂 = 30\) (cách chọn)

Vậy số tam giác có thể có là: 30 (tam giác)

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

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