{"common":{"save":0,"post_id":"6471","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7035","mon_id":"1158767","chapter_id":"1158892","post_id":"6471","question":"<p>\u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng AB v\u1edbi <span class=\"math-tex\">$A(1;2),B(4;3)$<\/span> có m\u1ed9t vect\u01a1 pháp tuy\u1ebfn là:<\/p>","options":["<strong>A. <\/strong><span class=\"math-tex\">$\\overrightarrow{n}=(1;3)$<\/span>","<strong>B. <\/strong><span class=\"math-tex\">$\\overrightarrow{n}=(3;1)$<\/span>","<strong>C. <\/strong><span class=\"math-tex\">$\\overrightarrow{n}=(-3;1)$<\/span>","<strong>D. <\/strong><span class=\"math-tex\">$\\overrightarrow{n}=(1;-3)$<\/span>"],"correct":"2","level":"3","hint":"","answer":"<p>\u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng AB thì vuông góc v\u1edbi AB nên có m\u1ed9t véct\u01a1 pháp tuy\u1ebfn là <span class=\"math-tex\">$\\overrightarrow{AB}=(3;1)$<\/span>.<\/p><p>Ch\u1ecdn<strong> <span style=\"color:#16a085;\">B. <\/span><\/strong><span style=\"color:#16a085;\"><span class=\"math-tex\">$\\overrightarrow{n}=(3;1)$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-01 03:03:35","option_type":"math","len":0},{"id":"7036","mon_id":"1158767","chapter_id":"1158892","post_id":"6471","question":"<p>\u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n AB v\u1edbi <span class=\"math-tex\">$A(1;-2),B(3;2)$<\/span> có ph\u01b0\u01a1ng trình là:<\/p>","options":["<strong>A. <span class=\"math-tex\">$x+2y-2=0$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$x-y-2=0$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$-x+y-2=0$<\/span><\/strong>","<strong>D. <span class=\"math-tex\">$x+2y+2=0$<\/span><\/strong>"],"correct":"1","level":"3","hint":"","answer":"<p>G\u1ecdi <span class=\"math-tex\">$I$<\/span> là trung \u0111i\u1ec3m c\u1ee7a AB thì <span class=\"math-tex\">$I(2;0)$<\/span>.<\/p><p>\u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n AB \u0111i qua trung \u0111i\u1ec3m <span class=\"math-tex\">$I(2;0)$<\/span> và vuông góc v\u1edbi v\u1edbi AB thì có véct\u01a1 pháp tuy\u1ebfn là <span class=\"math-tex\">$\\overrightarrow{AB}=(2;4)$<\/span>nên có ph\u01b0\u01a1ng trình là :<\/p><p><strong><span class=\"math-tex\">$2(x-2)+4(y-0)=0\\Leftrightarrow$<\/span> <span class=\"math-tex\">$x+2y-2=0$<\/span>.<\/strong><\/p><p>Ch\u1ecdn<strong> <span style=\"color:#16a085;\"><\/span><span style=\"color:#16a085;\">A. <span class=\"math-tex\">$x+2y-2=0$<\/span><\/span><\/strong><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-01 03:05:33","option_type":"math","len":0},{"id":"7040","mon_id":"1158767","chapter_id":"1158892","post_id":"6471","question":"<p>Cho tam giác ABC có <span class=\"math-tex\">$A(2;-2),B(2;0),C(4;2)$<\/span>. L\u1eadp ph\u01b0\u01a1ng trình \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam giác ABC k\u1ebb t\u1eeb A.<\/p>","options":["<strong>A. <span class=\"math-tex\">$-3x-y+8=0$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$3x+y-2=0$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$3x-y-8=0$<\/span><\/strong>","<strong>D. <span class=\"math-tex\">$3x-y+8=0$<\/span><\/strong>"],"correct":"3","level":"3","hint":"","answer":"<p>G\u1ecdi <span class=\"math-tex\">$I$<\/span> là trung \u0111i\u1ec3m c\u1ee7a BC thì <span class=\"math-tex\">$I(3;1)$<\/span>. Suy ra <span class=\"math-tex\">$\\overrightarrow{AI}=(1;3)$<\/span>.<\/p><p>\u0110\u01b0\u1eddng trung tuy\u1ebfn AI \u0111i qua trung \u0111i\u1ec3m <span class=\"math-tex\">$A(2;-2)$<\/span> và có véct\u01a1 pháp tuy\u1ebfn là <span class=\"math-tex\">$\\overrightarrow{n}=(3;-1)$<\/span> nên có ph\u01b0\u01a1ng trình là :<\/p><p><strong><span class=\"math-tex\">$3(x-2)-1(y+2)=0\\Leftrightarrow$<\/span> <span class=\"math-tex\">$3x-y-8=0$<\/span>.<\/strong><\/p><p>Ch\u1ecdn<strong> <span style=\"color:#16a085;\">C. <\/span><span style=\"color:#16a085;\"><span class=\"math-tex\">$3x-y-8=0$<\/span><\/span><span style=\"color:#16a085;\"><\/span><\/strong><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-01 03:42:59","option_type":"math","len":0}]}