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Giải bài 7.9 trang 32 sách bài tập toán 10 - Kết nối tri thức với cuộc sống

Nhà bạn Nam định đổi tủ lạnh và dự định kê vào vị trí dưới cầu thang.

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Đề bài

Nhà bạn Nam định đổi tủ lạnh và dự định kê vào vị trí dưới cầu thang. Biết vị trí kê tủ lạnh có mặt cát là một hình thang vuông với hai đáy lần lượt là 150 cm và 250 cm, chiều cao là 150 cm (như hình vẽ). Bố mẹ Nam định mua một tủ lạnh 2 cánh (Slide by slide) có chiều cao là 183 cm và bề ngang 90 cm. Bằng cách sử dụng tọa độ trong mặt phẳng, em hãy giúp Nam tính xem bố mẹ Nam có thể kê vừa chiếc tủ lạnh vào vị trí cần kê không?

Phương pháp giải - Xem chi tiết

Gắn hệ trục tọa độ \(Oxy\), đặt vị trí các điểm nút.

Lời giải chi tiết

+ Gắn hệ trục tọa độ như hình vẽ:

+ Để tận dung tối đa chiều cao thể khi kê tủ lạnh thì bố mẹ Nam sẽ kê tủ sát vào trục Oy, Do đó để kê được một chiếc tủ lạnh 2 cánh với bề ngang 90 cm thì chiều cao của tủ phải nhỏ hơn tung độ của điểm E thuộc đường thẳng BC với hoành độ điểm E bằng 90+ Ta có: \(B\left( {150;150} \right),C\left( {0;250} \right) \Rightarrow \overrightarrow {BC}  = \left( { - 150;100} \right) \Rightarrow \overrightarrow {{n_{BC}}}  = \left( {100;150} \right)\)+ Phương trình đường thẳng BC là: \(100\left( {x - 0} \right) + 150\left( {y - 250} \right) = 0 \Rightarrow 2x + 3y - 750 = 0\)+ Điểm E thuộc đường thẳng BC có hoành độ bằng 90 nên tung độ của E là 190+ Do 183 cm < 190 cm nên bố mẹ bạn Nam có thể kê chiếc tủ lạnh có bề ngang là 90 cm và chiều cao là 183 cm.

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