Question

12£®¶ÔÓÚƽÃæÖ±½Ç×ø±êϵÖеÄÈÎÒâÁ½µãA£¨a£¬b£©£¬B£¨c£¬d£©£¬ÎÒÃÇ°Ñ|a-c|+|b-d|½Ð×öA¡¢BÁ½µãÖ®¼äµÄÖ±½Ç¾àÀ룬¼Ç×÷d£¨A£¬B£©
£¨1£©ÒÑÖªO£¨0£¬0£©Îª×ø±êÔ­µã£¬ÈôµãP×ø±êΪ£¨-1£¬3£©£¬Çód£¨O£¬P£©£»
£¨2£©ÈôQ£¨x£¬y£©ÔÚµÚÒ»ÏóÏÞ£¬ÇÒÂú×ãd£¨O£¬Q£©=4£¬Çëд³öxÓëyÖ®¼äÂú×ãµÄ¹Øϵʽ£¬²¢ÔÚƽÃæÖ±½Ç×ø±êϵÄÚ»­³ö·ûºÏÌõ¼þµÄµãQ×é³ÉµÄͼÐΣ»
£¨3£©ÉèMÊÇÒ»¶¨µã£¬NÊÇÖ±Ïßy=mx+nÉϵĶ¯µã£¬ÎÒÃÇ°Ñd£¨M£¬N£©µÄ×îСֵ½Ð×öMµ½Ö±Ïßy=mx+nµÄÖ±½Ç¾àÀ룬ÊÔÇóµãM£¨2£¬-1£©µ½Ö±Ïßy=x+3µÄÖ±½Ç¾àÀ룮

Answer 1

·ÖÎö £¨1£©¸ù¾ÝÁ½µãÖ®¼äµÄÖ±½Ç¾àÀëµÄ¶¨Ò壬½áºÏO¡¢PÁ½µãµÄ×ø±ê¼´¿ÉµÃ³ö½áÂÛ£»
£¨2£©¸ù¾ÝÁ½µãÖ®¼äµÄÖ±½Ç¾àÀëµÄ¶¨Ò壬Óú¬x¡¢yµÄ´úÊýʽ±íʾ³öÀ´d£¨O£¬Q£©=4£¬½áºÏµãQ£¨x£¬y£©ÔÚµÚÒ»ÏóÏÞ£¬¼´¿ÉµÃ³ö½áÂÛ£»
£¨3£©ÓɵãNÔÚÖ±Ïßy=x+3ÉÏ£¬Éè³öµãNµÄ×ø±êΪ£¨m£¬m+3£©£¬Í¨¹ýÑ°ÕÒd£¨M£¬N£©µÄ×îСֵ£¬µÃ³öµãM£¨2£¬-1£©µ½Ö±Ïßy=x+3µÄÖ±½Ç¾àÀ룮

½â´ð ½â£º£¨1£©¸ù¾ÝÌâÒâµÃ£ºd£¨O£¬P£©=|0-£¨-1£©|+|0-3|=1+3=4£®
£¨2£©d£¨O£¬Q£©=4£¬¼´|x|+|y|=4£¬
ÓÖ¡ßQ£¨x£¬y£©ÔÚµÚÒ»ÏóÏÞ£¬
¡àx£¾0£¬y£¾0£¬
¡àxÓëyÖ®¼äÂú×ãµÄ¹ØϵʽΪ£ºx+y=4£¬
¼´y=-x+4£®
»­³öͼÐÎÈçÏ£®

£¨3£©¡ßµãNÔÚÖ±Ïßy=x+3ÉÏ£¬
¡àÉèµãNµÄ×ø±êΪ£¨m£¬m+3£©£¬
Ôò£ºd£¨M£¬N£©=|2-m|+|-1-£¨m+3£©|=|2-m|+|m+4|£¬
µ±m£¼-4ʱ£¬d£¨M£¬N£©=-2-2m£¾6£»
µ±-4¡Üm¡Ü2ʱ£¬d£¨M£¬N£©=6£»
µ±m£¾2ʱ£¬d£¨M£¬N£©=2m+2£¾6£®
¹Êd£¨M£¬N£©µÄ×îСֵΪ6£®
´ð£ºµãM£¨2£¬-1£©µ½Ö±Ïßy=x+3µÄÖ±½Ç¾àÀëΪ6£®

µãÆÀ ±¾Ì⿼²éÁËÒ»´Îº¯ÊýµÄÓ¦Óᢻ­Ò»´Îº¯ÊýµÄͼÏóÒÔ¼°Ç󺬾ø¶ÔÖµºÅµÄÒ»´Î·½³ÌµÄ×îÖµ£¬½âÌâµÄ¹Ø¼ü£º£¨1£©Ì×Óö¨ÒåÖеĹ«Ê½£»£¨2£©Ì×Óö¨ÒåÖеĹ«Ê½²¢½áºÏ¾ßÌåÇé¿ö»­³öÒ»´Îº¯ÊýͼÐΣ»£¨3£©·ÖmµÄ²»Í¬Çé¿öÑ°ÕÒ×îÖµ£®±¾ÌâÊôÓÚÖеµÌ⣬ÄѶȲ»´ó£¬Ö»ÒªÄܹ»¶Á¶®ÌâÖеÄж¨Ò壬Äܹ»ÔËÓö¨ÒåÖиø¶¨µÄ¹«Ê½½â¾öÎÊÌâ¼´¿É£®