ÌâÄ¿ÄÚÈÝ
Èçͼ£¬ÔÚƽÃæÖ±½Ç×ø±êϵÖУ¬ËıßÐÎOABCΪֱ½ÇÌÝÐΣ¬OA¡ÎBC£¬BC=14£¬A£¨16£¬0£©£¬C£¨0£¬2£©£®£¨1£©Èçͼ¢Ù£¬ÈôµãP¡¢Q·Ö±ð´ÓµãC¡¢Aͬʱ³ö·¢£¬µãPÒÔÿÃë2¸öµ¥Î»µÄËÙ¶ÈÓÉCÏòBÔ˶¯£¬µãQÒÔÿÃë4¸öµ¥Î»µÄËÙ¶ÈÓÉAÏòOÔ˶¯£¬µ±µãQÍ£Ö¹Ô˶¯Ê±£¬µãPҲֹͣÔ˶¯£®ÉèÔ˶¯Ê±¼äΪtÃ루0¡Üt¡Ü4£©£®
¢ÙÇóµ±tΪ¶àÉÙʱ£¬ËıßÐÎPQABΪƽÐÐËıßÐΣ¿
¢ÚÇóµ±tΪ¶àÉÙʱ£¬Ö±ÏßPQ½«ÌÝÐÎOABC·Ö³É×óÓÒÁ½²¿·ÖµÄ±ÈΪ1£º2£¬²¢Çó³ö´ËʱֱÏßPQµÄ½âÎöʽ£®
£¨2£©Èçͼ¢Ú£¬ÈôµãP¡¢Q·Ö±ðÊÇÏ߶ÎBC¡¢AOÉϵÄÈÎÒâÁ½µã£¨²»ÓëÏ߶ÎBC¡¢AOµÄ¶ËµãÖغϣ©£¬ÇÒËıßÐÎOQPCÃæ»ýΪ10£¬ÊÔ˵Ã÷Ö±ÏßPQÒ»¶¨¾¹ýÒ»¶¨µã£¬²¢Çó³ö¸Ã¶¨µãµÄ×ø±ê£®
·ÖÎö£º£¨1£©¢ÙÖ»ÒªPB=AQ¾Í˵Ã÷ËıßÐÎPQABΪƽÐÐËıßÐΣ¬Óɴ˽¨Á¢¹ØÓÚtµÄ·½³Ì£®
¢ÚÖ±ÏßPQ½«ÌÝÐÎOABC·Ö³É×óÓÒÁ½²¿·ÖµÄ±ÈΪ1£º2£¬ÔòÌÝÐÎCOQPµÄÃæ»ýÊÇÌÝÐÎCOABÃæ»ýµÄ
£®Óɴ˽¨Á¢¹ØÓÚtµÄ·½³Ì£®
£¨2£©Í¨¹ýÉèPµã×ø±ê£¬ÓÉÃæ»ýÒÑÖª¿É±íʾQµã×ø±ê£¬ÕâÑù¿É±íʾ³öÖ±ÏßPQµÄ½âÎöʽ£¬È»ºó·ÖÎö½âÎöʽÕÒ³ö¶¨µã£®
¢ÚÖ±ÏßPQ½«ÌÝÐÎOABC·Ö³É×óÓÒÁ½²¿·ÖµÄ±ÈΪ1£º2£¬ÔòÌÝÐÎCOQPµÄÃæ»ýÊÇÌÝÐÎCOABÃæ»ýµÄ
1 |
3 |
£¨2£©Í¨¹ýÉèPµã×ø±ê£¬ÓÉÃæ»ýÒÑÖª¿É±íʾQµã×ø±ê£¬ÕâÑù¿É±íʾ³öÖ±ÏßPQµÄ½âÎöʽ£¬È»ºó·ÖÎö½âÎöʽÕÒ³ö¶¨µã£®
½â´ð£º½â£º£¨1£©¢ÙCP=2t£¬ÔòPB=14-2t£¬AQ=4tÒòΪPB¡ÎQA£¬
ËùÒÔµ±PB=QAʱËıßÐÎPQABΪƽÐÐËıßÐΣ¬¼´ÓÐ14-2t=4t£®
ËùÒÔt=
s
¢ÚÖ±ÏßPQ½«ÌÝÐÎOABC·Ö³É×óÓÒÁ½²¿·ÖµÄ±ÈΪ1£º2£¬ÔòÌÝÐÎCOQPµÄÃæ»ýÊÇÌÝÐÎOABCÃæ»ýµÄ
£¬
¡à
£¨2t+16-4t£©¡Á2=
¡Á
(14+16)¡Á2£¬
¼´t=3sʱ£¬Ö±ÏßPQ·ÖÌÝÐÎOABC×óÓÒÁ½²¿·ÖµÄ±ÈΪ1£º2
´ËʱP£¨6£¬2£©£¬Q£¨4£¬0£©¿ÉÇóµÃPQ£ºy=x-4£®
£¨2£©ÉèµãPµÄ×ø±êΪ£¨m£¬2£©£¬ÔòCP=m£®
¡ßËıßÐÎOQPCÃæ»ýΪ10£¬
¡à
(m+OQ)•2=10£¬½âµÃOQ=10-m£®
¡àQ£¨10-m£¬0£©£®
ÉèÖ±ÏßPQµÄ½âÎöʽΪy=kx+b£¬£¨k¡Ù0£©£¬
Ôò
£¬Á½Ê½Ïà¼ÓµÃb=1-5k£®
¡àÖ±ÏßPQµÄ½âÎöʽ¿É±íʾΪy=kx+1-5k£®
ÓÉÓÚÉÏʽÖе±x=5ʱ£¬y=1£¬ÓëkµÄÈ¡ÖµÎ޹أ¬
¼´²»ÂÛkÈ¡ÈκÎÂú×ãÌõ¼þµÄÖµ£¬Ö±ÏßPQ±Ø¹ý¶¨µã£¨5£¬1£©£®
ËùÒÔµ±PB=QAʱËıßÐÎPQABΪƽÐÐËıßÐΣ¬¼´ÓÐ14-2t=4t£®
ËùÒÔt=
7 |
3 |
¢ÚÖ±ÏßPQ½«ÌÝÐÎOABC·Ö³É×óÓÒÁ½²¿·ÖµÄ±ÈΪ1£º2£¬ÔòÌÝÐÎCOQPµÄÃæ»ýÊÇÌÝÐÎOABCÃæ»ýµÄ
1 |
3 |
¡à
1 |
2 |
1 |
3 |
1 |
2 |
¼´t=3sʱ£¬Ö±ÏßPQ·ÖÌÝÐÎOABC×óÓÒÁ½²¿·ÖµÄ±ÈΪ1£º2
´ËʱP£¨6£¬2£©£¬Q£¨4£¬0£©¿ÉÇóµÃPQ£ºy=x-4£®
£¨2£©ÉèµãPµÄ×ø±êΪ£¨m£¬2£©£¬ÔòCP=m£®
¡ßËıßÐÎOQPCÃæ»ýΪ10£¬
¡à
1 |
2 |
¡àQ£¨10-m£¬0£©£®
ÉèÖ±ÏßPQµÄ½âÎöʽΪy=kx+b£¬£¨k¡Ù0£©£¬
Ôò
|
¡àÖ±ÏßPQµÄ½âÎöʽ¿É±íʾΪy=kx+1-5k£®
ÓÉÓÚÉÏʽÖе±x=5ʱ£¬y=1£¬ÓëkµÄÈ¡ÖµÎ޹أ¬
¼´²»ÂÛkÈ¡ÈκÎÂú×ãÌõ¼þµÄÖµ£¬Ö±ÏßPQ±Ø¹ý¶¨µã£¨5£¬1£©£®
µãÆÀ£ºÕÆÎÕƽÐÐËıßÐεÄÅж¨·½·¨£®¼ÇסÌÝÐεÄÃæ»ý¹«Ê½£®ÕÆÎÕÓôý¶¨ÏµÊý·¨ÇóÖ±ÏߵĽâÎöʽ£®¶ÔÓÚÇ󶨵ãµÄÎÊÌâ¿ÉÓò»¶¨µÄ½âµÃµ½ÈçÉÏÌ⣺y=kx+1-5k£¬Ôò£¨x-5£©k=y-1£¬ÓëkµÄÈ¡ÖµÎ޹ؼ´kÓÐÎÞÊý¸öÖµ£¬ËùÒÔx-5=0£¬y-1=0£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿