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HomeLớp 10Toán lớp 10 - Sách Kết nối tri thứcBài 20. Đường thẳng trong mặt phẳng tọa độBài tập nâng cao
{"common":{"save":0,"post_id":"6481","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7122","mon_id":"1158767","chapter_id":"1158892","post_id":"6481","question":"<p>Trong m\u1eb7t ph\u1eb3ng to\u1ea1 \u0111\u1ed9 Oxy, kho\u1ea3ng cách t\u1eeb \u0111i\u1ec3m M(0; 2) \u0111\u1ebfn<br \/>\u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$\\Delta$<\/span>: sinα.x + cosα.y + 2(2 – cosα) = 0 b\u1eb1ng <\/p>","options":["<strong>A.<\/strong> 2","<strong>B.<\/strong> 2sinα","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{2}{cos\\alpha+sin\\alpha}$<\/span>","<strong>D.<\/strong> 4"],"correct":"4","level":"3","hint":"","answer":"<p>Kho\u1ea3ng cách t\u1eeb \u0111i\u1ec3m M(0; 2) \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$\\Delta$<\/span>: sinα.x + cosα.y + 2(2 – cosα) = 0 là<\/p><p>d(M; <span class=\"math-tex\">$\\Delta$<\/span>) = <span class=\"math-tex\">$\\dfrac{|0.sin\\alpha+2.cos\\alpha+2(2-cos\\alpha)|}{\\sqrt{sin^2\\alpha+cos^2\\alpha}}$<\/span> = 4.<\/p><p>\u0110áp án \u0111úng là <span style=\"color:#16a085;\"> <strong>D.<\/strong> 4.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-03 09:09:13","option_type":"math","len":0},{"id":"7124","mon_id":"1158767","chapter_id":"1158892","post_id":"6481","question":"<p>Kho\u1ea3ng cách t\u1eeb giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng x – y + 2 = 0 và x + 3y – 2 = 0 \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$\\Delta$<\/span>: 2x + 3y + 4 = 0 b\u1eb1ng <\/p>","options":["<strong>A.<\/strong> 2<span class=\"math-tex\">$\\sqrt{10}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{3\\sqrt{13}}{5}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{5\\sqrt{13}}{13}$<\/span>","<strong>D.<\/strong> 2"],"correct":"3","level":"3","hint":"","answer":"<p>To\u1ea1 \u0111\u1ed9 giao \u0111i\u1ec3m M c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng x – y + 2 = 0 và x + 3y – 2 = 0 là nghi\u1ec7m h\u1ec7<\/p><p><span class=\"math-tex\">$\\begin{cases}x-y+2=0\\\\x+3y-2=0\\end{cases}$<\/span> ⇔ <span class=\"math-tex\">$\\begin{cases}x=-1\\\\y=1\\end{cases}$<\/span> ⇒ M(–1; 1)<\/p><p>d(M; <span class=\"math-tex\">$\\Delta$<\/span>) = <span class=\"math-tex\">$\\dfrac{|2.(-1)+3.1+4|}{\\sqrt{2^2+3^2}}$<\/span> = <span class=\"math-tex\">$\\dfrac{5\\sqrt{13}}{13}$<\/span> .<\/p><p>\u0110áp án \u0111úng là <span style=\"color:#16a085;\"><strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{5\\sqrt{13}}{13}$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-03 09:20:23","option_type":"math","len":0},{"id":"7125","mon_id":"1158767","chapter_id":"1158892","post_id":"6481","question":"<p>Trong m\u1eb7t ph\u1eb3ng to\u1ea1 \u0111\u1ed9 Oxy, cho tam giác ABC có A(1; 2), B(0; –3) và C(4; 0).<\/p><p>Chi\u1ec1u cao c\u1ee7a tam giác k\u1ebb t\u1eeb \u0111\u1ec9nh A b\u1eb1ng <\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{17}{5}$<\/span>","<strong>B.<\/strong> 3","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{1}{25}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{3}{5}$<\/span>"],"correct":"1","level":"3","hint":"","answer":"<p>\u0110\u01b0\u1eddng th\u1eb3ng \u0111i qua hai \u0111i\u1ec3m B(0; –3) và C(4; 0) có ph\u01b0\u01a1ng trình –3x + 4y + 12 = 0.<\/p><p><span class=\"math-tex\">$h_A$<\/span> = d(A; BC) = <span class=\"math-tex\">$\\dfrac{|-3.1+4.2+12|}{\\sqrt{(-3)^2+4^2}}$<\/span> = <span class=\"math-tex\">$\\dfrac{17}{5}$<\/span>.<\/p><p>\u0110áp án \u0111úng là <span style=\"color:#16a085;\"> <strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{17}{5}$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-03 09:42:09","option_type":"math","len":0}]}