19£®ÈçͼËùʾ£¬½«ÁâÐÎABCD·ÅÖÃÓÚÆ½ÃæÖ±½Ç×ø±êϵÖУ¬ÆäÖÐAB±ßÔÚyÖáÉÏ£¬µãC×ø±êΪ£¨4£¬0£©£®Ö±Ïßm£º$y=-\frac{4}{3}x-3$¾­¹ýµãB£¬½«¸ÃÖ±ÏßÑØ×ÅyÖáÒÔÿÃë1¸öµ¥Î»µÄËÙ¶ÈÏòÉÏÆ½ÒÆ£¬ÉèÆ½ÒÆÊ±¼äΪt£¬¾­¹ýµãDÊ±Í£Ö¹Æ½ÒÆ£®
£¨1£©Ìî¿Õ£ºµãDµÄ×ø±êΪ£¨4£¬5£©£»
£¨2£©ÉèÆ½ÒÆÊ±¼äΪt£¬ÇóÖ±Ïßm¾­¹ýµãA¡¢C¡¢D µÄʱ¼ät£»
£¨3£©ÒÑÖªÖ±ÏßmÓëBCËùÔÚÖ±Ïß»¥Ïà´¹Ö±£¬ÔÚÆ½Òƹý³ÌÖУ¬Ö±Ïßm±»ÁâÐΠABCD ½ØµÃÏ߶εij¤¶ÈΪl£¬Çëд³ölÓëÆ½ÒÆÊ±¼ätµÄº¯Êý¹ØÏµ±í´ïʽ£¨²»±ØÐ´³öÏêϸµÄ½â´ð¹ý³Ì£¬¼òҪ˵Ã÷ÄãµÄ½âÌâ˼·£¬Ð´Çå½á¹û¼´¿É£©£®

·ÖÎö £¨1£©ÏÈÇó³öBCµÄ³¤¼´¿É½â¾öÎÊÌ⣮
£¨2£©Çó³öA¡¢C¡¢D×ø±ê£¬ÀûÓôý¶¨ÏµÊý·¨¼´¿É¼´¿É£®
£¨3£©·ÖÈý¸öʱ¼ä¶ÎÌÖÂÛ¼´¿É¢Ùµ±0¡Üt¡Ü5ʱ£¬¢Úµ±5£¼t¡Ü$\frac{25}{3}$ʱ£¬¢Ûµ±$\frac{25}{3}$£¼t¡Ü$\frac{40}{3}$ʱ£¬·Ö±ð»­³öͼÏ󼴿ɽâ¾öÎÊÌ⣮

½â´ð ½â£º£¨1£©¡ßC£¨4£¬0£©£¬B£¨0£¬-3£©£¬
¡àOC=4£¬OB=3£¬
¡àBC=$\sqrt{O{C}^{2}+O{B}^{2}}$=$\sqrt{{3}^{2}+{4}^{2}}$=5£¬
¡ßËıßÐÎABCDÊÇÁâÐΣ¬
¡à£»BC=CD=5BC=CD=5£¬
¡àµãDµÄ×ø±êΪ£¨4£¬5£©£®
¹Ê´ð°¸Îª£¨4£¬5£©£®

£¨2£©¡ß$y=-\frac{4}{3}x-3$
¡àB£¨0£¬-3£©£¬OB=3
¡ßC£¨4£¬0£©
¡àOC=4£¬
Óɹ´¹É¶¨ÀíBC=5£¬¼´ÁâÐα߳¤ÊÇ5£¬µãA£¨0£¬2£©
Ö±Ïßm£º$y=-\frac{4}{3}x-3$´ÓµãB£¨0£¬-3£©¿ªÊ¼ÑØ×ÅyÖáÏòÉÏÆ½ÒÆ£¬
ÉèÆ½ÒÆ¹ý³ÌÖÐÖ±ÏßmµÄº¯Êý±í´ïʽΪ$y=-\frac{4}{3}x+b$£¬Ö±ÏßmÓëyÖá½»µãΪM£¬ÔòBM=t
µ±Ö±Ïßm£º$y=-\frac{4}{3}x+b$¾­¹ýµãA£¨0£¬2£©Ê±£º
MÓëAÖØºÏ£¬t=BM=BA=5£» 
µ±Ö±Ïßm£º$y=-\frac{4}{3}x+b$¾­¹ýµãC£¨4£¬0£©Ê±£º$y=-\frac{4}{3}x+\frac{16}{3}$£¬´ËʱM×ø±êΪ£¨0£¬$\frac{16}{3}$£©£¬t=BM=$\frac{25}{3}$£»
µ±Ö±Ïßm£º$y=-\frac{4}{3}x+b$¾­¹ýµãD£¨4£¬5£©Ê±£º$y=-\frac{4}{3}x+\frac{31}{3}$£¬´ËʱM×ø±êΪ£¨0£¬$\frac{31}{3}$£©£¬t=BM=$\frac{40}{3}$£»

£¨3£¬Èçͼ1£ºÉèÖ±Ïßm½»yÖáÓÚM£¬
½»BCÓÚN£¬Ôòl=MN£¬BM=t

¡ßÔÚÆ½Òƹý³ÌÖÐÖ±ÏßmÓëBCËùÔÚÖ±Ïß»¥Ïà´¹Ö±
ÏÔÈ»¡÷BNM¡×¡÷BOC£¬$\frac{MN}{OC}=\frac{BM}{BC}$
¡ßOC=4£¬BC=5¡àl=MN=$\frac{4}{5}t$£¬
¢Úµ±5£¼t¡Ü$\frac{25}{3}$ʱ£¬Èçͼ2ÖУ¬ÉèÖ±Ïßm½»yÖáÓÚM£¬½»BCÓÚN£¬
½»ADÓÚP£¬´Ëʱ£ºl=NP£¬BM=t
¹ýAµã×÷AE¡ÍBCÓÚE£¬ÔòAE=PN=l£®

´Ëʱ¡÷AEB¡Õ¡÷COB£¬AE=OC=4
¡àl=4£¬
¢Ûµ±$\frac{25}{3}$£¼t¡Ü$\frac{40}{3}$ʱ£¬Èçͼ3ÖУ¬ÉèÖ±Ïßm½»yÖáÓÚM£¬½»ADÓÚP£¬
½»CDÓÚN£¬´Ëʱ£ºl=PN£¬BM=t£¬MA=t-5
¹ýNµã×÷NF¡ÎBC½»yÖáÓÚF£¬ÔòFN=BC=5£®

ÓÉ¡÷MFN¡×¡÷CBO£¬µÃ$\frac{MN}{OC}=\frac{FN}{BO}$£¬MN=$\frac{20}{3}$£»
ÓÉ¡÷MAP¡×¡÷CBO£¬µÃ $\frac{MP}{CO}=\frac{MA}{CB}$£¬MP=$\frac{4}{5}£¨{t-5}£©$
l=PN=MN-MP=$\frac{32}{3}-\frac{4}{5}t$£¬
×ÛÉÏËùÊö£º$l=\left\{\begin{array}{l}\;\frac{4}{5}t\;\;£¨µ±0¡Üt¡Ü5ʱ£©\\ 4\;\;£¨µ±5£¼t¡Ü\frac{25}{3}ʱ£©\\ \;\frac{32}{3}-\frac{4}{5}t\;\;£¨µ±\frac{25}{3}£¼t¡Ü\frac{40}{3}ʱ£©\end{array}\right.$£®

µãÆÀ ±¾Ì⿼²éÒ»´Îº¯Êý×ÛºÏÌâ¡¢ÁâÐεÄÐÔÖÊ¡¢ÏàËÆÈý½ÇÐεÄÅж¨ºÍÐÔÖÊ¡¢¹´¹É¶¨Àí£¬½âÌâµÄ¹Ø¼üÊÇÁé»îÓ¦Óôý¶¨ÏµÊý·¨£¬Ñ§»á·ÖÀàÌÖÂÛ£¬ÀûÓÃÏàËÆÈý½ÇÐεÄÐÔÖʽâ¾öÎÊÌ⣬ÊôÓÚÖп¼Ñ¹ÖáÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

9£®ÈôÒ»Ôª¶þ´Î·½³ÌµÄÁ½¸ùx1£¬x2Âú×ãÏÂÁйØÏµ£ºx1•x2+x1+x2+2=0£¬x1•x2-2x1-2x2+5=0£¬ÔòÕâ¸öÒ»Ôª¶þ´Î·½³ÌΪx2+3x+1=0£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

10£®Èçͼ£¬±ß³¤Îª4µÄÕý·½ÐÎABCDµÄ¶Ô³ÆÖÐÐÄÊÇ×ø±êÔ­µãO£¬AB¡ÎxÖᣬBC¡ÎyÖᣬ·´±ÈÀýº¯Êýy=$\frac{2}{x}$Óëy=-$\frac{2}{x}$µÄͼÏó¾ùÓëÕý·½ÐÎABCDµÄ±ßÏཻ£¬ÔòͼÖÐÒõÓ°²¿·ÖµÄÃæ»ýÖ®ºÍÊÇ£¨¡¡¡¡£©
A£®2B£®4C£®6D£®8

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

7£®ÏÂÁз½³Ì×éÖУ¬ÊôÓÚ¶þÔªÒ»´Î·½³Ì×éµÄÊÇ£¨¡¡¡¡£©
A£®$\left\{\begin{array}{l}{x+y=5}\\{y=2}\end{array}\right.$B£®$\left\{\begin{array}{l}{x+y=2}\\{y-z=8}\end{array}\right.$C£®$\left\{\begin{array}{l}{xy=4}\\{y=1}\end{array}\right.$D£®$\left\{\begin{array}{l}{{x}^{2}-1=0}\\{x+y=3}\end{array}\right.$

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

14£®ÔÚÏÂÁÐͼÐÎÐÔÖÊÖУ¬Æ½ÐÐËıßÐβ»Ò»¶¨¾ß±¸µÄÊÇ£¨¡¡¡¡£©
A£®Á½×é¶Ô±ß·Ö±ðÏàµÈB£®Á½×é¶Ô±ß·Ö±ðƽÐÐ
C£®¶Ô½ÇÏßÏàµÈD£®¶Ô½ÇÏß»¥ÏàÆ½·Ö

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

4£®Èçͼ£¬±ß³¤Îª1µÄÕý·½ÐÎOABCµÄ¶¥µãOÎª×ø±êÔ­µã£¬µãAÔÚxÖáµÄÕý°ëÖáÉÏ£¬µãCÔÚyÖáµÄÕý°ëÖáÉÏ£®¶¯µãDÔÚÏß¶ÎBCÉÏÒÆ¶¯£¨²»ÓëB£¬CÖØºÏ£©£¬Á¬½ÓOD£¬¹ýµãD×÷DE¡ÍOD£¬½»±ßABÓÚµãE£¬Á¬½ÓOE£®¼ÇCDµÄ³¤Îªt£®
£¨1£©µ±t=$\frac{1}{3}$ʱ£¬ÇóÖ±ÏßDEµÄº¯Êý±í´ïʽ£º
£¨2£©Èç¹û¼ÇÌÝÐÎCOEBµÄÃæ»ýΪS£¬ÄÇôÊÇ·ñ´æÔÚSµÄ×î´óÖµ£¿Èô´æÔÚ£¬ÇëÇó³öÕâ¸ö×î´óÖµ¼°´ËʱtµÄÖµ£»Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£»
£¨3£©µ±OD2+DE2È¡×îСֵʱ£¬ÇóµãEµÄ×ø±ê£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

11£®Èçͼ£¬ÒÑÖªËıßÐÎABCDÊÇÆ½ÐÐËıßÐΣ¬P¡¢QÊǶԽÇÏßBDÉϵÄÁ½¸öµã£¬ÇëÔÚÌâÄ¿ÖÐÌí¼ÓºÏÊʵÄÌõ¼þ£¬¾Í¿ÉÒÔÖ¤Ã÷£ºAP=CQ£®
£¨1£©ÄãÌí¼ÓµÄÌõ¼þÊÇBP=DQ£»
£¨2£©ÇëÄã¸ù¾ÝÌâÄ¿ÖеÄÌõ¼þºÍÄãÌí¼ÓµÄÌõ¼þÖ¤Ã÷AP=CQ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

8£®Èçͼ£¬¶þ´Îº¯Êýy=ax2+bx+cµÄͼÏóÓëxÖáÏཻÓÚµãA£¨-3£¬0£©ºÍµãB£¬ÓëyÖá½»ÓÚµãC£¬¶¥µãDµÄ×ø±êΪ£¨-1£¬4£©£®µãPÊǵڶþÏóÏÞÄÚÅ×ÎïÏßÉϵÄÒ»¶¯µã£¬¹ýµãP×öPM¡ÍxÖáÓÚM£¬½»Ïß¶ÎACÓÚµãE£®
£¨1£©Çó¸Ã¶þ´Îº¯ÊýµÄ½âÎöʽºÍÖ±ÏßACµÄ½âÎöʽ£»
£¨2£©µ±¡÷PACÃæ»ýΪ3ʱ£¬ÇóµãPµÄ×ø±ê£»
£¨3£©¹ýµãP×÷PQ¡ÎAB½»Å×ÎïÏßÓÚµãQ£¬¹ýµãQ×÷QN¡ÍxÖáÓÚN£®ÈôµãPÔÚµãQ×ó±ß£¬µ±¾ØÐÎPQMNµÄÖܳ¤×î´óʱ£º¢ÙÇóEMµÄ³¤£»¢ÚÖ±½ÓÅжϡ÷PCEÊÇÊ²Ã´ÌØÊâÈý½ÇÐΣ®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

9£®·½³Ì×é$\left\{\begin{array}{l}{x+y=10}\\{2x+y=16}\end{array}\right.$µÄ½âÊÇ£¨¡¡¡¡£©
A£®$\left\{\begin{array}{l}{x=5}\\{y=5}\end{array}\right.$B£®$\left\{\begin{array}{l}{x=6}\\{y=4}\end{array}\right.$C£®$\left\{\begin{array}{l}{x=2}\\{y=8}\end{array}\right.$D£®$\left\{\begin{array}{l}{x=7}\\{y=2}\end{array}\right.$

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸