Èçͼ1£¬Å×ÎïÏßy=ax2-5ax+4¾­¹ý¡÷ABCµÄÈý¸ö¶¥µã£¬ÒÑÖªBC¡ÎxÖᣬµãAÔÚxÖáÉÏ£¬µãCÔÚyÖáÉÏ£¬ÇÒAC=BC£®
£¨1£©ÇóÅ×ÎïÏߵĽâÎöʽ£»

£¨2£©ÈôµãPÊÇÅ×ÎïÏ߶ԳÆÖáÉÏÇÒÔÚxÖáÏ·½µÄ¶¯µã£¬ÊÇ·ñ´æÔÚ¡÷PABÊǵÈÑüÈý½ÇÐΣ¬Èô´æÔÚ£¬Çó³öËùÓзûºÏÌõ¼þµÄµãP×ø±ê£»²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£»
£¨3£©Èçͼ2£¬½«¡÷AOCÑØxÖá¶ÔÕ۵õ½¡÷AOC1£¬ÔÙ½«¡÷AOC1ÈÆƽÃæÄÚijµãÐýת180¡ãºóµÃ¡÷A1O1C2£¨A£¬O£¬C1·Ö±ðÓëµãA1£¬O1£¬C2¶ÔÓ¦£©Ê¹µãA1£¬C2ÔÚÅ×ÎïÏßÉÏ£¬ÇóA1£¬C2µÄ×ø±ê£®
·ÖÎö£º£¨1£©ÁîÅ×ÎïÏß½âÎöʽÖÐx=0£¬Çó³ö¶ÔÓ¦µÄyµÄÖµ£¬¼´ÎªCµÄ×Ý×ø±ê£¬È·¶¨³öCµÄ×ø±ê£¬ÔÙÓÉBCÓëxÖáƽÐУ¬µÃµ½BµÄ×Ý×ø±êÓëCµÄ×Ý×ø±êÏàµÈ£¬°Ñ´ËʱµÄ×Ý×ø±ê´úÈëÅ×ÎïÏß½âÎöʽÇó³öxµÄÖµ£¬µÃµ½BµÄºá×ø±ê£¬È·¶¨³öBµÄ×ø±ê£¬ÓÖAC=BC£¬ÓÉBCµÄ³¤µÃµ½ACµÄ³¤£¬ÔÚÖ±½ÇÈý½ÇÐÎAOCÖУ¬ÓÉAC¼°OCµÄ³¤£¬ÀûÓù´¹É¶¨ÀíÇó³öOAµÄ³¤£¬È·¶¨³öAµÄ×ø±ê£¬°ÑAµÄ×ø±ê´úÈëÅ×ÎïÏß½âÎöʽÖУ¬Áгö¹ØÓÚaµÄ·½³Ì£¬Çó³ö·½³ÌµÄ½âµÃµ½aµÄÖµ£¬¼´¿ÉÈ·¶¨³öÅ×ÎïÏߵĽâÎöʽ£»
£¨2£©·ÖÈýÖÖÇé¿ö¿¼ÂÇ£º¢ÙÒÔABΪÑüÇÒ¶¥½ÇΪ¡ÏAʱ£¬ÓÐAB=AP1£¬¹ýB×÷BN¡ÍxÖᣬÉèÅ×ÎïÏ߶ԳÆÖáÓëxÖá½»ÓÚM£¬ÇÒÓÉÅ×ÎïÏß½âÎöʽÇó³ö¶Ô³ÆÖᣬÓÉOA+ONÇó³öANµÄ³¤£¬ÔÚÖ±½ÇÈý½ÇÐÎABNÖУ¬ÓÉAN£¬BN£¬ÀûÓù´¹É¶¨ÀíÇó³öABµÄ³¤£¬¼´ÎªAP1µÄ³¤£¬ÔÚÖ±½ÇÈý½ÇÐÎAMP1ÖУ¬ÓÉAP1¼°AMµÄ³¤£¬ÀûÓù´¹É¶¨ÀíÇó³öP1MµÄ³¤£¬ÔÙ¸ù¾ÝP1Ϊ¶Ô³ÆÖáÉϵĵ㼰ΪµÚËÄÏóÏ޵ĵ㣬µÃ³öP1µÄ×ø±ê£»¢ÚÒÔABΪÑüÇÒ¶¥½ÇΪ¡ÏBʱ£¬ÓÐAB=BP2£¬Í¬ÀíBP2µÄ³¤£¬ÔÚRt¡÷BQP2ÖУ¬¸ù¾Ý¹´¹É¶¨ÀíÇó³öQP2µÄ³¤£¬ÔÙÓÉQMµÈÓÚBµÄ×Ý×ø±ê£¬Çó³öMP2µÄ³¤£¬ÔÙ¸ù¾ÝP2Ϊ¶Ô³ÆÖáÉϵĵ㼰ΪµÚËÄÏóÏ޵ĵ㣬µÃ³öP2µÄ×ø±ê£»¢ÛÒÔABΪµ×£¬¶¥½ÇΪ¡ÏPʱ£¬P3ΪÏ߶ÎABµÄ´¹Ö±Æ½·ÖÏßÓëÅ×ÎïÏ߶ԳÆÖáµÄ½»µã£¬ÓÖAC=BC£¬¹ÊCÒ²ÔÚÏ߶ÎABµÄ´¹Ö±Æ½·ÖÏßÉÏ£¬
¼´Ö±ÏßCP3ΪÏ߶ÎABµÄ´¹Ö±Æ½·ÖÏߣ¬ÓÉAºÍBµÄ×ø±ê£¬ÀûÓÃÖеã×ø±ê¹«Ê½Çó³öABÖеãµÄ×ø±ê£¬Éè³öÏ߶ÎAB´¹Ö±Æ½·ÖÏߵķ½³ÌΪy=kx+b£¬°ÑCºÍÏ߶ÎABµÄÖеã´úÈëµÃµ½¹ØÓÚkÓëbµÄ·½³Ì×飬Çó³ö·½³Ì×éµÄ½âµÃµ½kÓëbµÄÖµ£¬È·¶¨³öÏ߶ÎAB´¹Ö±Æ½·ÖÏߵķ½³Ì£¬½«¶Ô³ÆÖáxµÄÖµ´úÈëÇó³öyµÄÖµ£¬¼´ÎªP3µÄ×Ý×ø±ê£¬½ø¶øÈ·¶¨³öP3µÄ×ø±ê£»
£¨3£©ÓÉÅ×ÎïÏߵĶԳÆÐԵõ½Å×ÎïÏߵĶԳÆÖáÓëxÖáµÄ½»µãMΪ¶Ô³ÆÖÐÐÄ£¬¼´MΪAA1µÄÖе㣬MΪC1C2µÄÖе㣬ÓÉC¹ØÓÚyÖáµÄ¶Ô³ÆÐԵõ½C1µÄ×ø±ê£¬ÔÙÓÉAºÍMµÄ×ø±ê£¬ÀûÓÃÖеã×ø±ê¹«Ê½¼´¿ÉÇó³öC2¼°A1µÄ×ø±ê£®
½â´ð£º½â£º£¨1£©ÁîÅ×ÎïÏßy=ax2-5ax+4ÖÐx=0£¬ÇóµÃy=4£¬
¡àC£¨0£¬4£©£¬ÓÖBC¡ÎxÖᣬ
¡àBµÄ×Ý×ø±êΪ4£¬
°Ñy=4´úÈëy=ax2-5ax+4µÃ£ºax2-5ax=0£¬¼´ax£¨x-5£©=0£¬
½âµÃ£ºx=0£¨ÉáÈ¥£©»òx=5£¬
¡àBµÄ×ø±êΪ£¨5£¬4£©£¬
¡àBC=5£¬ÓÖAC=BC£¬
¡àAC=5£¬ÓÖOC=4£¬
ÔÚRt¡÷AOCÖУ¬¸ù¾Ý¹´¹É¶¨ÀíµÃ£ºOA=
AC2-OC2
=3£¬
¡àA£¨-3£¬0£©£¬
°Ñx=-3£¬y=0´úÈëy=ax2-5ax+4µÃ£º9a+15a+4=0£¬
½âµÃ£ºa=-
1
6
£¬
ÔòÅ×ÎïÏß½âÎöʽΪy=-
1
6
x2+
5
6
x+4£»


£¨2£©´æÔÚ·ûºÏÌõ¼þµÄµãP£¬¹²ÓÐ3¸ö£¬
¢ÙÒÔABΪÑüÇÒ¶¥½ÇΪ¡ÏAʱ£¬ÓÐAB=AP1£¬
¹ýB×÷BN¡ÍxÖᣬÉèÅ×ÎïÏ߶ԳÆÖáÓëxÖá½»ÓÚM£¬
ÓÉÅ×ÎïÏßy=-
1
6
x2+
5
6
x+4£¬µÃµ½¶Ô³ÆÖáΪx=
5
2
£¬
ÓÖ¡ßA£¨-3£¬0£©£¬B£¨5£¬4£©£¬
¡àOA=3£¬ON=5£¬BN=4£¬
¡àAN=OA+ON=8£¬
ÔÚRt¡÷ABNÖУ¬ÀûÓù´¹É¶¨ÀíµÃ£ºAB=
AN2+BN2
=4
5
£¬
¡àAP1=4
5
£¬ÓÖAM=3+
5
2
=
11
2
£¬
ÔÚRt¡÷AMP1ÖУ¬¸ù¾Ý¹´¹É¶¨ÀíµÃ£ºMP1=
AP12-AM2
=
199
2
£¬
ÔòP1£¨
5
2
£¬-
199
2
£©£»
¢ÚÒÔABΪÑüÇÒ¶¥½ÇΪ¡ÏBʱ£¬ÓÐAB=BP2£¬Í¬ÀíBP2=4
5
£¬
ÓÖBQ=
1
2
BC=
5
2
£¬QM=4£¬
ÔÚRt¡÷BQP2ÖУ¬¸ù¾Ý¹´¹É¶¨ÀíµÃ£ºQP2=QM+MP2=
BP22-QB2
£¬
¡à4+MP2=
295
2
£¬¼´MP2=
295
-8
2
£¬
ÔòP2£¨
5
2
£¬
8-
295
2
£©£»
¢ÛÒÔABΪµ×£¬¶¥½ÇΪ¡ÏPʱ£¬P3ΪÏ߶ÎABµÄ´¹Ö±Æ½·ÖÏßÓëÅ×ÎïÏ߶ԳÆÖáµÄ½»µã£¬
ÓÖ¡ßAC=BC£¬¹ÊCÒ²ÔÚÏ߶ÎABµÄ´¹Ö±Æ½·ÖÏßÉÏ£¬
¼´Ö±ÏßCP3ΪÏ߶ÎABµÄ´¹Ö±Æ½·ÖÏߣ¬
ÓÉAºÍBµÄ×ø±ê£¬µÃµ½Ï߶ÎABµÄÖеãW×ø±êΪ£¨
5-3
2
£¬
0+4
2
£©£¬¼´£¨1£¬2£©£¬
ÓÖ¡ßC£¨0£¬4£©£¬
ÉèÖ±ÏßWCµÄ·½³ÌΪ£ºy=kx+b£¬
°ÑWºÍCµÄ×ø±ê´úÈëµÃ£º
k+b=2
b=4
£¬
½âµÃ£ºk=-2£¬b=4£¬
¡àÏ߶ÎAB´¹Ö±Æ½·ÖÏߵķ½³ÌΪy=-2x+4£¬
½«x=
5
2
´úÈëµÃ£ºy=-2¡Á
5
2
+4=-1£¬
ÔòP3£¨
5
2
£¬-1£©£¬
×ÛÉÏ£¬Âú×ãÌâÒâµÄPÓÐÈý¸ö£¬·Ö±ðΪ£ºP1£¨
5
2
£¬-
199
2
£©£»P2£¨
5
2
£¬
8-
295
2
£©£»P3£¨
5
2
£¬-1£©£»

£¨3£©ÓÉÅ×ÎïÏߵĶԳÆÐԵõ½£º¶Ô³ÆÖáÓëxÖáµÄ½»µãMΪ¶Ô³ÆÖÐÐÄ£¬
¸ù¾Ý¶Ô³ÆÐԵõ½£ºC1M=C2M£¬AM=A1M£¬
¡ßA£¨-3£¬0£©£¬M£¨
5
2
£¬0£©£¬
¡àA1µÄ×ø±êΪ£¨2¡Á
5
2
+3£¬0£©£¬¼´£¨8£¬0£©£¬
ÓÖ¡ßC£¨0£¬4£©£¬
¡àC1£¨0£¬-4£©£¬ÓÖM£¨
5
2
£¬0£©£¬
¡àC2µÄ×ø±êΪ£¨2¡Á
5
2
-0£¬2¡Á0+4£©£¬¼´£¨5£¬4£©£®
µãÆÀ£º´ËÌâÊôÓÚ¶þ´Îº¯ÊýµÄ×ÛºÏÌ⣬Éæ¼°µÄ֪ʶÓУº¶þ´Îº¯ÊýµÄÐÔÖÊ£¬ÀûÓôý¶¨ÏµÊý·¨Çóº¯ÊýµÄ½âÎöʽ£¬µãµÄ×ø±ê£¬µÈÑüÈý½ÇÐεÄÐÔÖÊ£¬Ï߶δ¹Ö±Æ½·ÖÏßµÄÐÔÖÊ£¬Ï߶εÄÖеã×ø±ê¹«Ê½£¬¹´¹É¶¨Àí£¬ÒÔ¼°ÕÛµþ¡¢ÐýתµÄÐÔÖÊ£¬ÀûÓÃÁËת»¯£¬·ÖÀàÌÖÂÛ¼°ÊýÐνáºÏµÄ˼Ï룬ÊÇÒ»µÀ×ÛºÏÐÔÇ¿¡¢½ÏÄѵÄÌ⣬ҪÇóѧÉúÕÆÎÕ֪ʶҪȫÃ森
Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

¾«Ó¢¼Ò½ÌÍøÒÑÖª¶þ´Îº¯ÊýµÄͼÏóÊǾ­¹ýµãA£¨1£¬0£©£¬B£¨3£¬0£©£¬E£¨0£¬6£©ÈýµãµÄÒ»ÌõÅ×ÎïÏߣ®
£¨1£©ÇóÕâÌõÅ×ÎïÏߵĽâÎöʽ£»
£¨2£©Èçͼ£¬ÉèÅ×ÎïÏߵĶ¥µãΪC£¬¶Ô³ÆÖá½»xÖáÓÚµãD£¬ÔÚyÖáÕý°ëÖáÉÏÓÐÒ»µãP£¬ÇÒÒÔA¡¢O¡¢PΪ¶¥µãµÄÈý½ÇÐÎÓë¡÷ACDÏàËÆ£¬ÇóPµãµÄ×ø±ê£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÔĶÁÀí½â

¾«Ó¢¼Ò½ÌÍøÔĶÁ²ÄÁÏ£ºÈçͼ1£¬¹ý¡÷ABCµÄÈý¸ö¶¥µã·Ö±ð×÷³öÓëˮƽÏß´¹Ö±µÄÈýÌõÖ±Ïߣ¬Íâ²àÁ½ÌõÖ±ÏßÖ®¼äµÄ¾àÀë½Ð¡÷ABCµÄ¡°Ë®Æ½¿í¡±£¨a£©£¬ÖмäµÄÕâÌõÖ±ÏßÔÚ¡÷ABCÄÚ²¿Ï߶εij¤¶È½Ð¡÷ABCµÄ¡°Ç¦´¹¸ß¡±£¨h£©£®ÎÒÃǿɵóöÒ»ÖÖ¼ÆËãÈý½ÇÐÎÃæ»ýµÄз½·¨£ºS¡÷ABC=
12
ah£¬¼´Èý½ÇÐÎÃæ»ýµÈÓÚˮƽ¿íÓëǦ´¹¸ß³Ë»ýµÄÒ»°ë£®
½â´ðÏÂÁÐÎÊÌ⣺
Èçͼ2£¬Å×ÎïÏ߶¥µã×ø±êΪµãC£¨1£¬4£©£¬½»xÖáÓÚµãA£¨3£¬0£©£¬µãPÊÇÅ×ÎïÏߣ¨ÔÚµÚÒ»ÏóÏÞÄÚ£©ÉϵÄÒ»¸ö¶¯µã£®
£¨1£©ÇóÅ×ÎïÏߵĽâÎöʽ£»
£¨2£©ÈôµãBΪÅ×ÎïÏßÓëyÖáµÄ½»µã£¬ÇóÖ±ÏßABµÄ½âÎöʽ£»
£¨3£©ÔÚ£¨2£©µÄÌõ¼þÏ£¬ÉèÅ×ÎïÏߵĶԳÆÖá·Ö±ð½»AB¡¢xÖáÓÚµãD¡¢M£¬Á¬½ÓPA¡¢PB£¬µ±PµãÔ˶¯µ½¶¥µãCʱ£¬Çó¡÷CABµÄǦ´¹¸ßCD¼°S¡÷CAB£»
£¨4£©ÔÚ£¨2£©µÄÌõ¼þÏ£¬ÉèPµãµÄºá×ø±êΪx£¬¡÷PABµÄǦ´¹¸ßΪh¡¢Ãæ»ýΪS£¬Çë·Ö±ðд³öhºÍS¹ØÓÚxµÄº¯Êý¹Øϵʽ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

£¨1£©Èçͼ1£¬¾ØÐÎABCD£¬µãCÓë×ø±êÔ­µãOÖغϣ¬µãAÔÚxÖáÉÏ£¬µãB×ø±êΪ£¨3£¬
3
£©£¬Çó¾­¹ýA¡¢B¡¢CÈýµãÅ×ÎïÏߵĽâÎöʽ£»
£¨2£©Èçͼ2£¬Å×ÎïÏßE£ºy=-
1
2
x2+bx+c
¾­¹ý×ø±êÔ­µãO£¬Æ䶥µãÔÚyÖá×ó²à£¬ÒÔOΪ¶¥µã×÷¾ØÐÎOADC£¬A¡¢CΪÅ×ÎïÏßEÉÏÁ½µã£¬ÈôAC¡ÎxÖᣬAD=2CD£¬ÔòÅ×ÎïÏߵĽâÎöʽÊÇ
 
£»
£¨3£©Èçͼ3£¬µãA¡¢B¡¢C·Ö±ðΪÅ×ÎïÏßF£ºy=ax2+bx+c£¨a£¼0£©Éϵĵ㣬µãBÔÚ¶Ô³ÆÖáÓҲ࣬µãDÔÚÅ×ÎïÏßÍ⣬˳´ÎÁ¬½ÓA¡¢B¡¢C¡¢DËĵ㣬Ëù³ÉËıßÐÎΪ¾ØÐΣ¬ÇÒAC¡ÎxÖᣬAD=2CD£¬Çó¾ØÐÎABCDµÄÖܳ¤£¨Óú¬aµÄʽ×Ó±íʾ£©£®
¾«Ó¢¼Ò½ÌÍø

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

Èçͼ£¬½«Å×ÎïÏßy=-
1
2
x2
ƽÒƺ󾭹ýÔ­µãOºÍµãA£¨6£¬0£©£¬Æ½ÒƺóµÄÅ×ÎïÏߵĶ¥µãΪµãB£¬¶Ô³ÆÖáÓëÅ×ÎïÏßy=-
1
2
x2
ÏཻÓÚµãC£¬ÔòͼÖÐÖ±ÏßBCÓëÁ½ÌõÅ×ÎïÏßΧ³ÉµÄÒõÓ°²¿·ÖµÄÃæ»ýΪ£¨¡¡¡¡£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÔĶÁÀí½â

ÔĶÁ²ÄÁÏ£º
Èçͼ1£¬¹ý¡÷ABCµÄÈý¸ö¶¥µã·Ö±ð×÷³öÓëˮƽÏß´¹Ö±µÄÈýÌõÖ±Ïߣ¬Íâ²àÁ½ÌõÖ±ÏßÖ®¼äµÄ¾àÀë½Ð¡÷ABCµÄ¡°Ë®Æ½¿í¡±£¨a£©£¬ÖмäµÄÕâÌõÖ±ÏßÔÚ¡÷ABCÄÚ²¿Ï߶εij¤¶È½Ð¡÷ABCµÄ¡°Ç¦´¹¸ß¡±£¨h£©£®ÎÒÃǿɵóöÒ»ÖÖ¼ÆËãÈý½ÇÐÎÃæ»ýµÄз½·¨£ºS¡÷ABC=ah£¬¼´Èý½ÇÐÎÃæ»ýµÈÓÚˮƽ¿íÓëǦ´¹¸ß³Ë»ýµÄÒ»°ë£®

½â´ðÏÂÁÐÎÊÌ⣺
Èçͼ2£¬Å×ÎïÏ߶¥µã×ø±êΪµãC£¨1£¬4£©£¬½»xÖáÓÚµãA£¨3£¬0£©£¬µãPÊÇÅ×ÎïÏߣ¨ÔÚµÚÒ»ÏóÏÞÄÚ£©ÉϵÄÒ»¸ö¶¯µã£®
£¨1£©ÇóÅ×ÎïÏߵĽâÎöʽ£»
£¨2£©ÈôµãBΪÅ×ÎïÏßÓëyÖáµÄ½»µã£¬ÇóÖ±ÏßABµÄ½âÎöʽ£»
£¨3£©ÉèµãPÊÇÅ×ÎïÏߣ¨µÚÒ»ÏóÏÞÄÚ£©ÉϵÄÒ»¸ö¶¯µã£¬ÊÇ·ñ´æÔÚÒ»µãP£¬Ê¹S¡÷PAB=S¡÷CAB£¿Èô´æÔÚ£¬Çó³öµãPµÄ×ø±ê£»Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸