{"common":{"save":0,"post_id":"7307","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7562","mon_id":"1158767","chapter_id":"1158861","post_id":"7307","question":"<p>Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy, cho hai \u0111i\u1ec3m A(&ndash;2; 4) v&agrave; B(8; 4). T&igrave;m t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m C thu\u1ed9c tr\u1ee5c ho&agrave;nh sao cho tam gi&aacute;c ABC vu&ocirc;ng t\u1ea1i C.<\/p>","options":["<strong>A.<\/strong> C(6; 0)","<strong>B.<\/strong> C(0; 0) ho\u1eb7c C(6; 0)","<strong>C.<\/strong> C(0; 0)","<strong>D.<\/strong> C(&ndash;1; 0) ho\u1eb7c C(0; 0)"],"correct":"2","level":"3","hint":"","answer":"<p>V&igrave; C thu\u1ed9c tr\u1ee5c Ox n&ecirc;n C(x; 0) v&agrave;&nbsp;<span class=\"math-tex\">$\\overrightarrow{CA}=(-2-x;4)$<\/span>,&nbsp;<span class=\"math-tex\">$\\overrightarrow{CB}=(8-x;4)$<\/span>.<\/p><p>\u0110\u1ec3 tam gi&aacute;c ABC vu&ocirc;ng t\u1ea1i C th&igrave;&nbsp;<span class=\"math-tex\">$\\overrightarrow{CA}.\\overrightarrow{CB}=0$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$(-2-x)(8-x)+16=0$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$x^2-6x=0$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$x=0$<\/span>&nbsp;ho\u1eb7c&nbsp;<span class=\"math-tex\">$x=6$<\/span>.<\/p><p>Khi \u0111&oacute;&nbsp;<span class=\"math-tex\">$C(0;0)$<\/span>&nbsp;ho\u1eb7c&nbsp;<span class=\"math-tex\">$C(6;0)$<\/span>.<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>B.<\/strong> C(0; 0) ho\u1eb7c&nbsp;C(6; 0).<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-21 01:12:24","option_type":"txt","len":2},{"id":"7563","mon_id":"1158767","chapter_id":"1158861","post_id":"7307","question":"<p>Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy, cho hai \u0111i\u1ec3m A(1; 2) v&agrave; B(&ndash;3; 1). T&igrave;m t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m C thu\u1ed9c tr\u1ee5c tung sao cho tam gi&aacute;c ABC vu&ocirc;ng t\u1ea1i A.<\/p>","options":["<strong>A.<\/strong> C(0; 6)","<strong>B.<\/strong> C(5; 0)","<strong>C.<\/strong> C(3; 1)","<strong>D.<\/strong> C(0; &ndash;6)"],"correct":"1","level":"3","hint":"","answer":"<p>V&igrave; C thu\u1ed9c tr\u1ee5c Oy n&ecirc;n C(0; y) v&agrave;&nbsp;<span class=\"math-tex\">$\\overrightarrow{AB}=(-4;-1)$<\/span>,&nbsp;<span class=\"math-tex\">$\\overrightarrow{AC}=(-1;y-2)$<\/span>.<\/p><p>\u0110\u1ec3 tam gi&aacute;c ABC vu&ocirc;ng t\u1ea1i A th&igrave;&nbsp;<span class=\"math-tex\">$\\overrightarrow{AB}.\\overrightarrow{AC}=0$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$4-(y-2)=0$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$y=6$<\/span><\/p><p>Khi \u0111&oacute; C(0; 6).<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>A.<\/strong> C(0; 6).<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-21 01:18:07","option_type":"txt","len":2},{"id":"7564","mon_id":"1158767","chapter_id":"1158861","post_id":"7307","question":"<p>Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy, cho ba \u0111i\u1ec3m A(&ndash;4; 0), B(&ndash;5; 0) v&agrave; C(3; 0). T&igrave;m \u0111i\u1ec3m M thu\u1ed9c tr\u1ee5c ho&agrave;nh sao cho&nbsp;<span class=\"math-tex\">$\\overrightarrow{MA}+\\overrightarrow{MB}+\\overrightarrow{MC}=\\overrightarrow{0}$<\/span>.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$M(-2;0)$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$M(2;0)$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$M(-4;0)$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$M(-5;0)$<\/span>"],"correct":"1","level":"3","hint":"","answer":"<p>V&igrave; M thu\u1ed9c tr\u1ee5c Ox n&ecirc;n M(x; 0).<\/p><p>Ta c&oacute;&nbsp;<span class=\"math-tex\">$\\overrightarrow{MA}=(-4-x;0)$<\/span>,&nbsp;<span class=\"math-tex\">$\\overrightarrow{MB}=(-5-x;0)$<\/span>,&nbsp;<span class=\"math-tex\">$\\overrightarrow{MC}=(3-x;0)$<\/span>.<\/p><p>Khi \u0111&oacute;&nbsp;<span class=\"math-tex\">$\\overrightarrow{MA}+\\overrightarrow{MB}+\\overrightarrow{MC}=\\overrightarrow{0}$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$(-6-3x;0)=(0;0)$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$-6-3x=0$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$x=-2$<\/span>.<\/p><p>V\u1eady M(&ndash;2; 0).<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>A.<\/strong>&nbsp;<span class=\"math-tex\">$M(-2;0)$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-21 01:26:05","option_type":"math","len":0}]}