II BAN VE VAN DE VE DO THI TRONG CAC BAI TOAN cue TRI TREN PHAN MEM HINH HOC DQNG CABRI ThS N g u y k Ngpc Giang Trong phdn mem hinh hgc Do dg ddi cdc dogn thdng ddng thi vide vg dd thj cua cdc CA, CB[.]
II BAN VE VAN DE VE DO THI TRONG CAC BAI TOAN cue TRI TREN P H A N MEM HINH HOC DQNG CABRI ThS N g u y k Ngpc Giang Trong phdn mem hinh hgc ddng thi vide vg dd thj cua cdc todn eye tii Id mgt cac van de thii vj vd khd hdc biia An chua tt9ng cdeh ve dd thj la nhieu didu khdng dan gidn Mdi quan hp giua dd thj ciia dgi Iugng cdn tim eye trj vdi Idi gidi bai lodn la mgt mdi quan he gdn bd va khaiig khit md ehung ta can tim hieu nhilu Bai vigt sau ddy sc di sau nghien cftu ban chat cua m9t sd edch dyng tren phan mgm hinh hgc dgng thdng qua mot so bdi todn ma chiing la thudng gap l.Bdil Cho hai didm A, B nam ve ciing phia ddi vdi dudng thang d Tim ttdn d mdt diem C choAC + CB nhd nhdt Tu bdi Todn hgc nay, ta dyng hinh tren phdn mem Hinh hpc ddng Cabri a Cdeh - Do dg ddi cdc dogn thdng CB CA, CB Budc 2: Tgo vet - Do long dp ddi cdc dogn - Tgo vet cho E, ehuyen thdng CA + CB ddng C ta thu dugc vet ciia - Dyng he tryc vudng gdc Oxy cho true Ox thuqc d dilm E Di chuyen didm E - Dyng trdn Oy mgt diem N cho ON bang tdng dg dai cho tung dg diem E be nhdt, ta thdy cdc gdc BCx vd ECx cdc dogn thdng CA + CB -.- Ggi giao didm ciia dudng bdng Nhu vdy ta nhan thay rdng vudng gdc vdi Oy ta! N vd dudng vudng gdc vdi Ox lgi C dk tim gid trj be nhdt ciia tdng la E (lung dd cua didm E bigu AC + CB ta ndn dyng dd thj diln sd tdng dg ddi cdc ciia gid trj n a y O each dyng thi ftng vdi mdi diem C trdn dogn thdng CA + CB) tryc Ox ta tim dugc mdt va chi Budc 2: Tgo vet - Tgo vet cho E, chuygn mgt diem N tedn tryc Oy (ON ddng C ta thu dugc vgt cua = CA + CB) Vi thl d day ta xae djnh dugc mdt ham sd y diem E Di chuyen didm E ^ f(x) Sau xae dinh dugc cho tung dp diem E be nhat, ham so ndy, ta se di ve thj la thdy cdc gdc ACd va BCx ciia ham sd Tft dd thj cua ham so la se tim dugc dai lugng bang Ngodi each dung d ttdn cdn can tim be nhat Tft vi tri cua dgi lugng can tim be nhat cd cdc each dung sau: ta se thay dugc vi tef cua diem b Cach C trdn dudng thang d Tu tim ldi giai cua bai loan Q each dung Id khdc so vdi each dyng Chiing ta khdng can dyng mdt he tryc tga vudng gdc Oxy Chiing la chi can dung tia AC va ttdn dd dyng didm E chp AE = AC + CB Sau ve thi cua dilm E Tft dd thj cua diem E ta sg tim thdy dugc gid tri cua AE be nhdt Tuomg ung vdi Budc 1: Dung hinh gid trj AE be nhdt ta se tim - Dyng dudng thdng d thdy vj tti cua didm C Tu - Dyng dilm A, dyng diem suy ldi gidi cua bai toan Budc 1: Dung hinh B ndm cimg phfa ddi vdi d - Dyng dudng thang d Ldi gidi cua bdi todn - Dyng diem C tren dudng -,Dimg dilm A, dung digm nhu sau thdng d B ndm cimg phia ddi vdi d Lay diem A' ddi xiing vdi -Ndi CA, CB, dung lia AC ,- Dyng diem C tten dudng Dyng ttdn tia AC mgt A qua d Khi dd AC = A'C Do thdng d dd AC + BC ngan nhat yd dilm E cho AE = AC + -NdiCA.CB chi A'C + BC ngan nhdt TAP CHf THIET BI GIAO DUC-SO 89-01/2013 • 39 Hay B C, AVthdng hing Sau ddy ta sS gidi thich ca sd todn ciia cdeh dyng d tren Ta tjnh tiln hp tryc Ox Djty vc hp tryc O'x'y' cho O'x' thugc d vd tryc: 0'>^ vudng gdc vdi d di qua A Liic ndy vipc gidi thich dgi Iuong CA + CB dgi gia trj bd nhat d h^ tryc Oxy ciing hodn loan gidng nhu gidi thich dgi lui;mg CA + CB dgt gia tri be nhdt he tryc O'x'y" Bay gid ta se tim hdm bidu thj dgi Iugng CA + CB ttong hp tryc O'x'y' Trong hd true O'x'y' nay, ggi C(x; 0);'A(6; h); B(d; h') Khidd IACB ^ C A + C B - Sau ddy Id mOl bdi todn khdc tuong ly vdi bai todn I Bdi Hai thdn ndm d hai vj tti A vd B'l^ch mgt sdng (xem ring Iiai bd sdng Id hai dudng thdng^ong song) (hinh vg 5) Njjudi la dy djnh xdy mgt chide cau MN bac qua sdng (cd nhidn cau phdi vudng gdc vdi bd sdng) va ldm hai dogn dudng thdng tft A den M vd tft B den N Hay xdc djnh vi tri ciia chide eau MN cho AM + MN + NB ngdn nhal., Ta dyng hinh tten phan mem Cabri nhu sau: fl, Cach ylx' + h' + Vcd - ")' + tf Dieu kipn cd eye tidu '^'^'^ hay \ \ , \ + V(d-x)'th") dx d-x X A ' + h^ X d- ,/(d - X)' + h" „ : ; : ^ : : ; ^ X X -.0(Uc-CA;lcB - Dyng teen Oy diem Y choOY = AM-i-MN+NB - Cdc dudng vudng gdc vdi Oy tgi Y vd Ox tgi M cdt tgiL Bude Kiim chung Tgo vit cho dilm L, chuyin ddng diem M, ta sg thu dugc vet ciia dilm L Di chuyin dilm M din vj tri cho AM + MN -I- NIB Id bd nhdt Tu vj trf bd nhdt ndy, ta sg tim cdeh gidi tuong ftng cho nd Ta sd giai thich bdn chat ciia cdeh dyng I ndy Cdeh ldm tuang ly nhu edch dung cua bai loan Ta Ijnh tidn hp trye Oxy ve hp tryc O'x'y' cho tryc O'x' thugc bd sdng d dl qua M va tryc O'y' vudng gdc vdi d di qua A Luc ndy dgi lugng AM + MN + NB dgt gid tri be nhat d teong he tryc Oxy cung hodn lodn dugc gidi thich gidng nhu dgi lugng AM + MN + NB dgt gid tri be nhdt ttong hp true O'x'y' Ta ed ttong hp tryc O'x'y thi M(x ; 0); A(0 ; h); N(x ; n); B(d ; h') Liic ndy ham bidu thi tdng dg dai cdc dogn thdng AM + MN -I- NB Id y JxUh^ + lD|t J(d- x)^ + (h'-D)^ \ Day chfnh la co sd toan cda each dyng bdi Sau day la edeh dyng khdc Budc Dung hinh b Cach 1., !« Dyng eon sdng nhu hinh Dung hinh Budc suy sina = sinp hay a=p - Dyng sdng nhu hinh Tu day ta sg cd AC