Question

6£®Èçͼ£¬ÔÚƽÃæÖ±½Ç×ø±êϵxOyÖУ¬µãOΪ×ø±êÔ­µã£¬Õý·½ÐÎOABCµÄ±ßOA£¬OC·Ö±ðÔÚxÖᣬyÖáÉÏ£¬µãBµÄ×ø±êΪ£¨4£¬4£©£¬·´±ÈÀýº¯Êýy=$\frac{k}{x}$£¨x£¾0£¬k¡Ù0£©µÄͼÏó¾­¹ýÏ߶ÎBCµÄÖеãD£¬½»Õý·½ÐÎOABCµÄÁíÒ»±ßABÓÚµãE£®
£¨1£©ÇókµÄÖµ£»
£¨2£©Èçͼ¢Ù£¬ÈôµãPÊÇxÖáÉϵĶ¯µã£¬Á¬½ÓPE£¬PD£¬DE£¬µ±¡÷DEPµÄÖܳ¤×î¶Ìʱ£¬ÇóµãPµÄ×ø±ê£»
£¨3£©Èçͼ¢Ú£¬ÈôµãQ£¨x£¬y£©Ôڸ÷´±ÈÀýº¯ÊýµÄͼÏóÉÏÔ˶¯£¨²»ÓëµãDÖغϣ©£¬¹ýµãQ×÷OM¡ÍyÖᣬ´¹×ãΪM£¬×÷QN¡ÍBCËùÔÚÖ±Ïߣ¬´¹×ãΪN£¬¼ÇËıßÐÎCMQNµÄÃæ»ýΪS£¬ÇóS¹ØÓÚxµÄº¯Êý±í´ïʽ£¬²¢Ð´³öxµÄÈ¡Öµ·¶Î§£®

Answer 1

·ÖÎö £¨1£©Ê×Ïȸù¾ÝÌâÒâÇó³öCµãµÄ×ø±ê£¬È»ºó¸ù¾ÝÖеã×ø±ê¹«Ê½Çó³öDµã×ø±ê£¬ÓÉ·´±ÈÀýº¯Êýy=$\frac{k}{x}$£¨x£¾0£¬k¡Ù0£©µÄͼÏó¾­¹ýÏ߶ÎBCµÄÖеãD£¬Dµã×ø±ê´úÈë½âÎöʽÇó³ök¼´¿É£»
£¨2£©¸ù¾ÝÖá¶Ô³ÆµÄÐÔÖÊÕÒµ½µãPµÄλÖãº×÷µãE¹ØÓÚxÖáµÄ¶Ô³ÆµãE¡ä£¬Á¬½ÓDE¡ä£¬½»xÖáÓÚµãP£¬ÇóµÃÖ±ÏßDE¡äÓëxÖáµÄ½»µã×ø±ê¼´¿É£»
£¨3£©·ÖÁ½²½½øÐнâ´ð£¬¢Ùµ±QÔÚÖ±ÏßBCµÄÉÏ·½Ê±£¬¼´0£¼x£¼2£¬Èçͼ1£¬¸ù¾ÝS_{ËıßÐÎCMQN}=CN•QDÁгöS¹ØÓÚxµÄ½âÎöʽ£¬¢Úµ±QÔÚÖ±ÏßBCµÄÏ·½Ê±£¬¼´x£¾2£¬Èçͼ2£¬ÒÀÈ»¸ù¾ÝS_{ËıßÐÎCMQN}=CN•QDÁгöS¹ØÓÚxµÄ½âÎöʽ£®

½â´ð ½â£º£¨1£©Èçͼ¢Ù£¬¡ßÕý·½ÐÎOABCµÄ±ßOA¡¢OC·Ö±ðÔÚxÖá¡¢yÖáÉÏ£¬µãBµÄ×ø±êΪ£¨4£¬4£©£¬
¡àC£¨0£¬4£©£¬
¡ßDÊÇBCµÄÖе㣬
¡àD£¨2£¬4£©£¬
¡ß·´±ÈÀýº¯Êýy=$\frac{k}{x}$£¨x£¾0£¬k¡Ù0£©µÄͼÏó¾­¹ýµãD£¬
¡àk=8£»

£¨2£©Èçͼ¢Ù£¬×÷µãE¹ØÓÚxÖáµÄ¶Ô³ÆµãE¡ä£¬Á¬½ÓDE¡ä£¬½»xÖáÓÚµãP£¬
°Ñx=4´úÈëy=$\frac{8}{x}$£¬µÃy=2£¬ÔòE£¨4£¬2£©£®
¹ÊµãE¹ØÓÚxÖá¶Ô³ÆµÄµãE¡ä£¨4£¬-2£©£®
ÉèÖ±ÏßDE¡äµÄ·½³ÌΪy=kx+b£¨k¡Ù0£©£®
½«D£¨2£¬4£©£¬E¡ä£¨4£¬-2£©·Ö±ð´úÈëµÃµ½£º$\left\{\begin{array}{l}{2k+b=4}\\{4k+b=-2}\end{array}\right.$£¬
½âµÃ$\left\{\begin{array}{l}{k=-3}\\{b=10}\end{array}\right.$£®
¹ÊÖ±ÏßDE¡äµÄ·½³ÌΪy=-3x+10£®
µ±y=0ʱ£¬x=$\frac{10}{3}$£¬
¼´P£¨$\frac{10}{3}$£¬0£©£»

£¨3£©Èçͼ¢Ú£¬µ±QÔÚÖ±ÏßBCµÄÉÏ·½Ê±£¬¼´0£¼x£¼2£¬
Èçͼ1£¬¡ßµãQ£¨x£¬y£©Ôڸ÷´±ÈÀýº¯ÊýµÄͼÏóÉÏÔ˶¯£¬
¡ày=$\frac{8}{x}$£¬
¡àS_{ËıßÐÎCMQN}=CN•QD=x•£¨ $\frac{8}{x}$-4£©=8-4x£¨0£¼x£¼2£©£¬

Èçͼ¢Û£¬µ±QÔÚÖ±ÏßBCµÄÏ·½Ê±£¬¼´x£¾4£¬Í¬ÀíÇó³öS_{ËıßÐÎCMQN}=CN•QD=x•£¨4-$\frac{8}{x}$£©=4x-8£¨x£¾2£©£¬
×ÛÉÏS=$\left\{\begin{array}{l}{8-4x£¨0£¼x£¼2£©}\\{4x-8£¨x£¾2£©}\end{array}\right.$£®

µãÆÀ ±¾ÌâÖ÷Òª¿¼²é·´±ÈÀýº¯ÊýµÄ×ÛºÏÌâµÄ֪ʶ£¬½â´ð±¾ÌâµÄ¹Ø¼üÊÇÊìÁ·ÕÆÎÕ·´±ÈÀýº¯ÊýµÄÐÔÖÊ£¬½â´ð£¨3£©Îʵĺ¯Êý½âÎöʽÐèÒª·Ö¶ÎÇ󣬴ËÌâÄѶȲ»´ó