Uzifunda njani ulungelelwaniso kwinqwelomoya yeCartesian

Ulungelelwaniso kwinqwelomoya yeCartesian lubalulekile kumelo lwegraphic kunye nohlalutyo lwemathematika lwezinto kunye neengqikelelo kwimilinganiselo emibini. Ezi zilungelelaniso zenziwe ngamanani amabini abonisa indawo ehambelanayo yenqaku ngokubhekiselele kwii-axes zesalathiso zendiza. Kweli nqaku lobugcisa, siya kuphonononga ngokweenkcukacha inkqubo yokufunda ulungelelwaniso kwinqwelomoya yeCartesian, ukubonelela ngokuqonda okucacileyo nokucacileyo kwale ngcamango esisiseko kodwa eyimfuneko kwimathematika kunye nejometri.

1. Intshayelelo kwinkqubo yokulungelelanisa kwinqwelomoya yeCartesian

Inkqubo yokulungelelanisa kwinqwelomoya yeCartesian sisixhobo esisisiseko kwimathematika kunye nefiziksi. Ivumela amanqaku kunye ne-vectors ukuba amelwe kwi-plane-dimensional plane ngokusetyenziswa kwee-axis ezimbini ze-perpendicular, i-x-axis kunye ne-y-axis, enqumla kwindawo ebizwa ngokuba yimvelaphi. Ukuqonda ngokufanelekileyo le nkqubo, kuyimfuneko ukwazi iingcamango ezisisiseko kunye nemithetho elawulayo. Apha ngezantsi kukho izinto eziphambili zenkqubo yolungelelwaniso kwinqwelomoya yeCartesian:

1. U-x kunye no-y axes: Imigca engu-x kunye no-y yimigca emibini ethe ngqo ethe nkqo enqumla kwimvelaphi. I-x-axis inabela ngokuthe tye ukuya ekunene nasekhohlo, ngeli lixa i-axis ka-y isuka ngokuthe nkqo phezulu nasezantsi. Indawo nganye kwinqwelo-moya inokufumaneka ngokukodwa ngesibini esicwangcisiweyo (x, y), apho u-x emele indawo yenqaku ku-x-axis kwaye u-y umele indawo yenqaku ku-y-axis.

2. Iiquadrants: Inqwelomoya yeCartesian yohlulwe yangamacandelo amane abizwa ngokuba ziiquadrants. I-Quadrant I ibekwe phezulu ngasekunene kwinqwelomoya, i-quadrant II phezulu ekhohlo, i-quadrant III ezantsi ngasekhohlo, kunye ne-quadrant IV ezantsi ngasekunene. Ezi quadrants zisetyenziselwa ukucacisa indawo yenqaku ngokuchanekileyo ngakumbi. Umzekelo, ukuba inqaku likwiquadrant III, oko kuthetha ukuba ino-x ethabathayo kunye no-y othabathayo.

2. Ingcamango yokulungelelanisa kwinqwelomoya yeCartesian

Kwijometri, ulungelelwaniso ngamaxabiso amanani asetyenziselwa ukumela indawo yenqaku kwinqwelomoya. Kwinqwelomoya yeCartesian, iiasi ezimbini ezithe tyaba, i-x-axis (ethe tyaba) kunye ne-y-axis (ethe nkqo), zisetyenziselwa ukumisela indawo yenqaku.

Ukuze uqonde, kubalulekile ukuqonda indlela ii-axes ezimbini ezilungelelaniswe ngayo. I-x-axis inabela ekunene kumanani a-positive kwaye ekhohlo kumanani athabathayo. Umgca ongu-y-axis unyukela phezulu kumanani a-positive kwaye ezantsi kumanani athabathayo.

Xa kufunyanwa indawo ethile kwinqwelomoya yeCartesian, iperi eodolweyo (x, y) isetyenziswa apho ux emele indawo yenqaku ku-x-axis aze u-y amele indawo yenqaku ku-y-axis. Kubalulekile ukukhumbula ukuba indawo yemvelaphi ifumaneka kwindawo (0, 0), ephakathi kwee-axes ezimbini. Xa ulungelelanisa ulungelelwaniso kwinqwelo-moya yeCartesian, umgca othe nkqo uzotywa ukusuka kwindawo x ukuya kwi-axis engu-x kunye nomgca othe tye ukusuka kwindawo u-y ukuya kwi-axis ka-y, ngaloo ndlela kufunyanwa eyona ndawo ichanekileyo yenqaku kwinqwelomoya.

3. Ukufunda ulungelelwaniso lweCartesian: i-x-axis kunye no-y-axis

Ukuqonda ngokupheleleyo ukufunda ulungelelwaniso lweCartesian, kubalulekile ukuqonda ii-axes ezimbini ezisisiseko: i-x-axis kunye ne-y-axis. Ezi ntsimbi ziyimigca ethe tye enqumla kwindawo ebizwa ngokuba yimvelaphi. I-x-axis inabela ngokuthe tye ukuya ekunene kwaye ekhohlo ukusuka kwimvelaphi, ngelixa i-axis ka-y isuka ngokuthe nkqo phezulu nasezantsi ukusuka kwimvelaphi.

Ukufunda ulungelelwaniso lweCartesian yenqaku kwinqwelomoya, amanani akwi-x-axis kunye no-y-axis amelwe njengesibini esicwangcisiweyo (x, y). Ixabiso lika-x limele umgama othe tye wenqaku ukusuka kwimvelaphi, ngelixa u-y ixabiso limele umgama othe nkqo wenqaku ukusuka kwimvelaphi. Ngokomzekelo, ukuba sinenqaku P kwinqwelomoya kunye nezilungelelaniso (3, 4), kuthetha ukuba kumgama weeyunithi ezi-3 ukuya ekunene kunye neeyunithi ezi-4 ukusuka kwimvelaphi.

Isixhobo esiluncedo sokujonga nokufunda iCartesian coordinates yinqwelomoya yeCartesian. Iqulathe imigca emibini ye-perpendicular, emele u-x kunye no-y axes, kunye neseti yamanqaku abekwe ngokweendlela zazo. Ngokucwangcisa ezi ngongoma kwinqwelomoya, sinokubona ngokulula indawo ezikuyo kwaye siwabele ulungelelwaniso oluhambelanayo. Xa usenza izibalo okanye usombulula iingxaki ezibandakanya ulungelelwaniso lweCartesian, kuyanceda ukusebenzisa igridi kwinqwelomoya ukuququzelela umlinganiselo kunye nokubonakaliswa okubonakalayo kwamanqaku.

4. Intsingiselo yexabiso elilungileyo nelibi kwii-coordinates

Kubalulekile ukuqonda indawo kunye nesalathiso senqaku kwinkqubo yolungelelwaniso. Kulo mongo, amaxabiso amahle kunye namabi amela ukufuduswa kwindawo yesalathiso. Okulandelayo, kuya kucaciswa ngokweenkcukacha ukuba kuthetha ukuthini ukuba ixabiso libe lihle okanye libi kwizilungelelaniso.

1. Ulungelelwaniso oluhle: Ixabiso elincomekayo kwizilungelelanisi libonisa utshintsho ukuya ngasekunene okanye phezulu. kwinkqubo yolungelelwaniso. Umzekelo, ukuba sinendawo kwizilungelelanisi (3, 4), ixabiso elilungileyo kwi-axis engu-x libonisa ukuba inqaku liziyunithi ezi-3 ngasekunene kwemvelaphi, ngelixa ixabiso elilungileyo kwi-axis engu-y libonisa ukuba inqaku Iiyunithi ezi-4 ukusuka kwimvelaphi. Ke, indibaniselwano yamaxabiso amahle kuzo zombini izilungelelanisi ivumela indawo ukuba ibekwe kwaye iboniswe kwinkqubo yolungelelwaniso.

2. Ulungelelwaniso olubi: Ngakolunye uhlangothi, ixabiso elibi kwiziko libonisa ukutshintshela ngakwesobunxele okanye phantsi kwindlela yokulungelelanisa. Ukulandela umzekelo wangaphambili, ukuba sinendawo kwizilungelelanisi (-3, -4), ixabiso elingalunganga kwi-x-axis libonisa ukuba inqaku ziiyunithi ezi-3 ekhohlo kwimvelaphi, ngelixa ixabiso elingalunganga kwi x- i-axis kwaye ibonisa ukuba inqaku liziyunithi ezi-4 ukusuka kwimvelaphi. Ke, amaxabiso angalunganga kuzo zombini izilungelelanisi avumela indawo ukuba ibekwe kwaye iboniswe kwinkqubo yolungelelwaniso.

3. Ukubaluleka kolungelelwaniso lwamaxabiso: Amaxabiso alungelelanisayo afanelekileyo kunye angalunganga abalulekile ukumisela isalathiso kunye nemvakalelo yokushukuma kwendawo kwinkqubo yolungelelwaniso. Ezi xabiso zisinika ulwazi malunga nokuhamba okuthe tye kunye nokuthe nkqo, okusivumela ukuba siseke ubudlelwane besithuba kunye nokwenza izibalo ezichanekileyo kwiimeko ezahlukeneyo. Ukumela ngokufanelekileyo amaxabiso alungileyo kunye angalunganga kulungelelwaniso, kuyimfuneko ukulandela ingqungquthela esekiweyo, apho ii-axes ezilungileyo zitshintshela ekunene kwi-axis ka-x kwaye phezulu kwi-y-axis, ngelixa i-axes engalunganga itshintshela ekhohlo umgca ongu-x kunye nezantsi umgca ongu-y.

Isishwankathelo, amaxabiso amahle kunye namabi kwiindlela zokunxibelelanisa zibalulekile ekufumaneni nasekujongeni amanqaku kwinkqubo yolungelelwaniso. Amaxabiso afanelekileyo abonisa utshintsho ukuya ekunene okanye phezulu, ngelixa amaxabiso angalunganga abonisa utshintsho ukuya ekhohlo okanye ezantsi. La maxabiso akuvumela ukuba umisele isalathiso kunye nesalathiso sokuhamba kwendawo, kunye nokwenza izibalo ezichanekileyo kwizicelo ezahlukeneyo. Kubalulekile ukulandela ingqungquthela esekiweyo ukumela amaxabiso ngokufanelekileyo kulungelelwaniso.

5. Inkcazo yee-quadrants kwinqwelomoya yeCartesian

1. Inqwelomoya yeCartesian sisixhobo esisisiseko kwijometri kunye nealgebra. Oku kubandakanya igridi eyenziwe ngemigca emibini egobileyo eyaziwa ngokuba ziizembe. I-axis exwesileyo ibizwa ngokuba yi-x-axis, ngelixa i-axis ethe nkqo ibizwa ngokuba ngu-y-axis.
2. Kwinqwelomoya yeCartesian, iingongoma zifumaneka ngolungelelwaniso, ezime ngendlela yeebini ezicwangcisiweyo (x, y). Ixabiso lika-x libonisa indawo ethe tye yenqaku, ngelixa ixabiso lika-y libonisa indawo ethe nkqo. Omabini amaxabiso anokuba positive, negative okanye zero.
3. Ukuqonda ii-quadrants kwinqwelomoya yeCartesian, kufuneka sithathele ingqalelo iimpawu zolungelelwaniso. Ukuba inqaku likwiquadrant yokuqala, zombini ixabiso layo lika-x kunye no-y-xabiso li-positive. Kwiquadranti yesibini, ixabiso lika-x lithabatha kwaye u-y xabiso li-positive. Kwi-quadrant yesithathu, zombini ixabiso lika-x kunye no-y ixabiso alilunganga. Kwaye okokugqibela, kwiquadrant yesine, ixabiso lika-x lilungile kwaye u-y wexabiso uyalambatha.

Isishwankathelo, ii-quadrants kwinqwelomoya yeCartesian zisivumela ukuba sihlele amanqaku ngokweendlela zabo zokulungelelanisa kunye neendawo zabo ngokubhekiselele kwii-axes. Kubalulekile ukuqaphela imiqondiso ka-x kunye no-y amaxabiso ukumisela ukuba yeyiphi i-quadrant ingongoma ethile ekuyo. Ukuqonda olu luhlu kubalulekile ukusombulula iingxaki yejometri kunye nealgebra ebandakanya ukusetyenziswa kwenqwelomoya yeCartesian.

6. Indlela yokumisela indawo yenqaku usebenzisa ulungelelwaniso lweCartesian

Ukumisela indawo yenqaku usebenzisa ulungelelwaniso lweCartesian, kuyimfuneko ukulandela ezinye amanyathelo aphambili. Okokuqala, kubalulekile ukukhumbula ukuba inkqubo yolungelelwaniso lweCartesian ineentsimbi ezimbini ezithe ngqo kwenye enye: i-x-axis (ethe tye) kunye ne-y-axis (ethe nkqo).

Inyathelo lokuqala kukuchonga ulungelelwaniso lwale ngongoma kuthethwa ngayo. Olu lungelelaniso luya kunikwa ngamaxabiso amabini, elinye libe lelendawo ku-x-axis kwaye elinye libe lelendawo ku-y-axis. Umzekelo, ukuba inqaku linamakhonkco (3, 5), lithetha ukuba iiyunithi ezintathu ukuya ngasekunene kunye neeyunithi ezintlanu ukusuka kwimvelaphi yenkqubo yolungelelwaniso.

Nje ukuba ulungelelwaniso lwale nqaku luchongiwe, lunokumelwa ngokwemizobo kwinkqubo yolungelelwaniso lweCartesian. Ngoncedo lomlawuli kunye nekhampasi, umgca unokutsalwa ukusuka kwimvelaphi ukuya kwindawo efunwayo ngokweendlela ezibonisiweyo. Eli cebo liza kukuvumela ukuba ubonise ngokuchanekileyo indawo yenqaku ngokunxulumene no-x kunye no-y axes.

7. Imizekelo yolungelelwaniso lokufunda kwinqwelomoya yeCartesian

Kukho iindlela ezininzi zokufunda ulungelelwaniso kwinqwelomoya yeCartesian, eyimfuneko ekuqondeni nasekumeleni idatha kwinkqubo yolungelelwaniso. Okulandelayo, imizekelo esebenzayo iya kuboniswa ukubonisa indlela yokutolika nokufumana iingongoma kwinqwelomoya yeCartesian.

1. Ukufunda ulungelelwaniso lweCartesian: Ukufunda inqaku kwinqwelomoya yeCartesian, ulungelelwaniso lwe-x kunye no-y kufuneka ichongwe. Ulungelelwaniso luka-x lubhekisa kwindawo ethe tye yenqaku, ngelixa u-y ebonisa indawo ethe nkqo. Umzekelo, ukuba sinenqaku ku-(3, 2), u-x ulungelelanisa ngu-3 kwaye u-y ulungelelanisa u-2.

2. Ukubonakaliswa kolungelelwaniso olubi: Kwakhona kubalulekile ukuqaphela ukuba ulungelelwaniso lunokuba lubi. Kwinqwelomoya yeCartesian, amanqaku kwicala lasekhohlo lemvelaphi (0,0) anenegative x izinxibelelanisi, ngelixa amanqaku angezantsi kwemvelaphi eno-y othabathayo. Umzekelo, inqaku ku-(-2, -4) ziiyunithi ezimbini ngasekhohlo kwemvelaphi kunye neeyunithi ezine ngaphantsi kwayo.

3. Indawo yeNdawo Umzekelo: Masithi sinenqaku kwinqwelomoya yeCartesian enezilungelelaniso (5, -3). Ukufumana le ndawo, bala iiyunithi ezintlanu ukuya ekunene ukusuka kwimvelaphi kwaye wehle iiyunithi ezintathu ezantsi. Ngale ndlela, ufikelela kwindawo oyifunayo. Kubalulekile ukukhumbula ukuba iyunithi yomlinganiselo kufuneka ingaguquguquki kuzo zombini izembe ukwenzela umboniso ochanekileyo womzobo.

8. Ukubaluleka kolungelelwaniso lweCartesian kumelo lwegrafu lwedatha

Ukumelwa kwedatha sisixhobo esisisiseko kwimathematika nakwinzululwazi. Ulungelelwaniso lweCartesian ludlala indima ebalulekileyo kolu melo, njengoko luvumela amanqaku ukuba abekwe kwinqwelomoya ngendlela echanekileyo necwangcisiweyo. Ukuqonda ukubaluleka kolungelelwaniso lweCartesian kubalulekile ukutolika iigrafu kunye nokusombulula iingxaki ngempumelelo.

Ukusebenzisa ulungelelwaniso lweCartesian kwidatha yegrafu, kufuneka uqonde ezinye iikhonsepthi eziphambili. Okokuqala, kubalulekile ukuqonda inkqubo yeCartesian axis, equlathe imigca emibini yeperpendicular ebizwa ngokuba yi-X axis (horizontal) kunye neY axis (ethe nkqo). Amaxabiso olungelelwaniso abonakaliswe njengezibini ezicwangcisiweyo (x, y), apho ulungelelwaniso luka-x luhambelana nendawo ethe tye yenqaku kunye nolungelelwaniso lwe-y luhambelana nendawo yalo ethe nkqo.

Ukuboniswa kwegraphical kwedatha kusetyenziswa ulungelelwaniso lweCartesian lusekwe kumanqaku okucwangcisa kwinqwelomoya ngokusekwe kulungelelwaniso lwazo. La manqaku ke aqhagamshelwe ukwenza imigca, iigophe, okanye ezinye imiboniso yegraphical. Ukwenza igrafu iseti yedatha, la manyathelo alandelayo angalandelwa: 1) chonga uluhlu lwamaxabiso kwi-X kunye ne-Y axes ukuseka ubungakanani benqwelomoya; 2) inqume izibini eziyalelweyo ezihambelana nedatha eziza kumelwa; 3) fumana indawo nganye kwinqwelomoya ngokweendlela zayo; 4) qhagamshela amachaphaza ngokufanelekileyo ngokulandela iphethini yedatha.

9. Ukusebenzisa ulungelelwaniso ukubala umgama phakathi kwamanqaku amabini kwinqwelomoya yeCartesian

Ukubala umgama phakathi kwamanqaku amabini kwinqwelomoya yeCartesian, sinokusebenzisa ulungelelwaniso lwala manqaku. Inkqubo ibandakanya ukusetyenziswa kwefomula yomgama phakathi kwamanqaku amabini kwinqwelomoya, esekelwe kwingcamango yePythagorean.

Ukusombulula ingxaki, landela la manyathelo:

• 1. Chonga ulungelelwaniso lwamanqaku amabini kwinqwelomoya yeCartesian.
• 2. Sebenzisa ifomula yomgama phakathi kwamanqaku amabini: d = √((x2 – x1)^2 + (y2 – y1)^2), apho (x1, y1) kunye (x2, y2) zizinxulumanisi zamanqaku amabini. .
• 3. Faka endaweni yokulungelelanisa amaxabiso kwifomula kwaye ubale umphumo.

Kubalulekile ukukhumbula ukuba umgama phakathi kwamanqaku amabini uhlala unexabiso elihle. Ukuba amanqaku alele kwi-axis enye, umgama uya kulingana nomahluko opheleleyo we-coordinates kuloo mgca. Ukongeza, kukho izixhobo ezininzi ze-intanethi ezinokunceda ukubala umgama phakathi kwamanqaku amabini kwinqwelomoya yeCartesian ngokukhawuleza nangokuchanekileyo. Qiniseka ukuba uziqhelanisa nemizekelo eyahlukeneyo ukuze uphucule ukuqonda kwakho kunye nezakhono zakho kule ndawo yemathematika.

10. Inkcazo yokulungelelaniswa kwe-polar kunye nobudlelwane babo kunye nenkqubo yeCartesian

Ulungelelwaniso lwePolar yinkqubo yokulungelelanisa esetyenziselwa ukumela amanqaku kwinqwelomoya esebenzisa i-engile kunye nomgama weradial. Ngokungafaniyo nenkqubo yeCartesian, esebenzisa ux kunye no-y ulungelelaniso, inkqubo yolungelelwaniso lwepolar isebenzisa u-r kunye no-θ ulungelelaniso. Ulungelelwaniso lwe-r lumele umgama wenqaku ukusuka kwimvelaphi, ngelixa i-θ imele i-engile eyenziwe yi-vector edibanisa imvelaphi ukuya kwinqanaba malunga ne-positive x axis.

Ubudlelwane phakathi kolungelelwaniso lwepolar kunye nenkqubo yeCartesian inokuchazwa ngeefomula zemathematika. Ngokusebenzisa umsebenzi we-cosine kunye nomsebenzi wesine, ulungelelwaniso lwe-r lunokunxulumana nolungelelwaniso lweCartesian u-x kunye no-y. Ulungelelwaniso luka-x lufunyanwa ngokuphinda-phinda u-r ulungelelwaniso nge-cosine ye-engile θ, ngelixa ulungelelwaniso luka-y lufunyanwa ngokuphindaphinda ulungelelwaniso lwe-r nge-sine ye-engile θ.

I-polar coordinate system iluncedo ngakumbi ekuchazeni izenzeko ezine-circular symmetry. Ukongeza, isetyenziswa kwiindawo ezahlukeneyo ezifana nefiziksi, ubunjineli kunye nemathematika. Ukuguqula i-polar coordinates kwi-Cartesian coordinates, iindlela ezahlukeneyo zingasetyenziswa, ezifana ne-trigonometry okanye ukusetyenziswa kwezixhobo ze-software ezikhethekileyo. Ngokuqonda kakuhle ukulungelelaniswa kwe-polar kunye nobudlelwane babo kunye nenkqubo Cartesian, uya kuba nakho ukusombulula iingxaki zejometri kunye nezibalo ngokufanelekileyo ngakumbi!

11. Umahluko phakathi kweCartesian coordinate system kunye ne-polar coordinate system

Inkqubo yokulungelelaniswa kweCartesian kunye nepolar coordinate system ziinkqubo ezimbini ezisetyenziselwa ukukhangela amanqaku kwinqwelomoya. Zombini iinkqubo zineempawu ezahlukeneyo ezenza zibe luncedo kwiimeko ezahlukeneyo.

Kwinkqubo yokulungelelaniswa kweCartesian, amanqaku amelwe ngababini abacwangcisiweyo (x, y). I-axis ethe tye yaziwa ngokuba yi-x-axis, ngelixa i-axis ethe nkqo yaziwa ngokuba ngu-y-axis. Indawo yokuma kwenqaku imiselwa ngumgama osuka kwimvelaphi (0,0) kuzo zombini iizembe. Le nkqubo isetyenziswa ngokubanzi kwimathematika kunye nefiziksi njengoko ibonelela ngomelo oluchanekileyo lolungelelwaniso.

Ngakolunye uhlangothi, kwi-polar coordinate system, amanqaku amelwe nge-angle kunye nomgama. I-engile ilinganiswa ukusuka kwi-positive x-axis counterclockwise, ngelixa umgama ulinganiswa ukusuka kwimvelaphi. Le nkqubo iluncedo ngakumbi xa usebenza ngeengxaki ezibandakanya izangqa okanye i-symmetry ye-radial, njengoko ivumela inkcazo enembileyo yendawo yamanqaku.

12. Ukusetyenziswa kolungelelwaniso lweCartesian kwihlabathi lokwenyani

Ulungelelwaniso lweCartesian, olukwabizwa ngokuba yinkqubo yolungelelwaniso oluxande, sisixhobo esisisiseko emhlabeni yokwenene ukuchaza izikhundla kunye nokulinganisa imigama. Le nkqubo isetyenziswa ngokubanzi kwiindawo ezahlukeneyo, ukusuka kwisayensi kunye neteknoloji ukuya kwizakhiwo kunye nokuhamba.

A yezicelo Olona setyenziso luxhaphakileyo lwezilungelelaniso zeCartesian kukuhamba. Iinkqubo zokuma kwehlabathi (GPS) zixhomekeke kulungelelwaniso lweCartesian ukumisela eyona ndawo yento okanye umntu. Enkosi koku, sinokuhamba ngokuchanekileyo sisebenzisa izixhobo ezinje ngeefowuni eziphathwayo kunye nabahambi ngeenqwelo-mafutha.

Kwinjineli kunye noyilo lwezakhiwo, Ulungelelwaniso lweCartesian luyimfuneko kuyilo kunye nokwakhiwa kwezakhiwo. Ezi zilungelelaniso zivumela iingcali ukuba zibale imilinganiselo yesakhiwo, ukuzoba iiplani, kunye nokumisela indawo echanekileyo yezinto ezifana neentsika kunye nemiqadi. Ukongeza, ulungelelwaniso lweCartesian lukwasetyenziswa kuyilo lwesekethe ye-elektroniki kunye nenkqubo yerobhothi, ivumela indawo echanekileyo yokubekwa kwecandelo kunye nenkqubo esebenzayo.

13. Uqheliselo olusebenzayo lokuphucula ukuqonda kolungelelwaniso lokufunda kwinqwelomoya yeCartesian

Ukuphucula ukuqonda kolungelelwaniso lokufunda kwinqwelomoya yeCartesian, kubalulekile ukwenza uqheliselo olusebenzayo olusivumela ukuba sisebenzise iikhonsepthi zethiyori ezifundiweyo. Ngezantsi kukho eminye imisebenzi enokukunceda womeleze izakhono zakho kwesi sihloko.

1. Chonga ulungelelwaniso: Ukuqala, kubalulekile ukuziqhelanisa nesakhiwo senqwelomoya yeCartesian kwaye ufunde ukuchonga ulungelelwaniso lwenqaku. Yenza imithambo ekucela ukuba ufumane ulungelelwaniso lwamanqaku athile kwinqwelomoya. Unokusebenzisa izixhobo ze-intanethi ezifana neGeogebra ukujonga iimpendulo zakho.

2. Amanqaku eploti: Nje ukuba uqonde indlela yokufunda ulungelelwaniso kwinqwelomoya yeCartesian, ziqhelanise namanqaku egrafu. Thatha umthambo ekucela ukuba ukhangele amanqaku athile kwinqwelomoya kwaye uphinde inkqubo amatyeli amaninzi. Khumbula ukuba inani lokuqala lolungelelwaniso limela indawo ethe tye kwaye inani lesibini limela indawo ethe nkqo.

3. Ukusombulula iingxaki: Ukubeka izakhono zakho zokuqonda ezilungelelanisiweyo, lungisa iingxaki ezifuna ukusetyenziswa kwenqwelomoya yeCartesian. Zinokubandakanya iimeko apho ucelwe ukuba ufumane umgama phakathi kwamanqaku amabini okanye umisele ulungelelwaniso lwendawo yokuhlangana. Sebenzisa iikhonsepthi ezifundiweyo kunye nomsebenzi Inyathelo nenyathelo, ukuchonga ulungelelwaniso olubandakanyekayo kwingxaki nganye kunye nokusebenzisa imisebenzi eyimfuneko.

14. Izigqibo zokufunda kunye nokusetyenziswa kolungelelwaniso kwinqwelomoya yeCartesian

Ukuqukumbela, ukufunda nokusebenzisa ulungelelwaniso kwinqwelomoya yeCartesian bubuchule obusisiseko kwimathematika nakwiinkalo ezahlukeneyo zesayensi. Kulo lonke eli nqaku sixoxe ngeengcamango ezisisiseko zenqwelomoya yeCartesian, indlela yokufunda ukulungelelanisa, kunye nendlela yokuyisebenzisa ukumela amanqaku kunye nokusombulula iingxaki zejometri.

Ukufunda ulungelelwaniso kwinqwelo-moya yeCartesian, kubalulekile ukukhumbula ukuba i-axis ethe tye ibizwa ngokuba yi-axis engu-X kwaye i-axis ethe nkqo ibizwa ngokuba yi-Coordinates iboniswe ngokwezibini ezicwangcisiweyo (x, y), apho u-x i-axis I-yy yindawo ekwi-axis engu-Y Kubalulekile ukuthathela ingqalelo imiqondiso eyakhayo kunye nechaphazamiso ukufumana amanqaku ngokuchanekileyo kwinqwelomoya.

Xa usebenzisa ulungelelwaniso kwinqwelomoya yeCartesian, kuluncedo ukusebenzisa izixhobo ezininzi kunye nobuchule. Omnye wabo ngumgaqo wamanani, ovumela ukulinganisa umgama phakathi kwamanqaku kwindiza. Isikali sinokusetyenziswa ukubonisa amanqaku ngokomlinganiselo. Ukongeza, kubalulekile ukuqhelana neequadrants ezahlukeneyo zenqwelomoya kunye nendlela ezinxibelelana ngayo nolungelelwaniso oluhle kunye olubi.

Isishwankathelo, ukufunda nokusebenzisa ulungelelwaniso kwinqwelomoya yeCartesian kubalulekile ekuqondeni nasekusombululeni iingxaki zemathematika nezejiyometri. Ngeli nqaku, siye safunda ukufunda ukulungelelanisa, ukuqhelana nezixhobo kunye nobuchule obufunekayo ukuzisebenzisa ngokuchanekileyo, kwaye siqonde ukubaluleka kwee-quadrants ezahlukeneyo kwinqwelomoya. Qhubeka uziqhelanisa kunye nokuphuhlisa izakhono zakho ekusebenziseni ulungelelwaniso kwinqwelomoya yeCartesian ukuze uqonde obu buchule bubalulekileyo bezibalo!

Ukuqukumbela, ukuqonda indlela ulungelelwaniso olufundwa ngayo kwinqwelomoya yeCartesian ibalulekile kulo naluphi na uphononongo olubandakanya ukuhlalutya kwamanqaku kwinkqubo yolungelelwaniso olunamacala amabini. Ukukwazi ukutolika nokumela izinto kunye neziganeko kule nkqubo kubalulekile kwiinkalo ezifana nezibalo, ifiziksi, ubunjineli kunye nejografi, phakathi kwezinye.

Ngokulawula le ngcamango, siya kukwazi ukufumana ngokuchanekileyo indawo kunye nokuchaza indawo yayo nayiphi na indawo kwinqwelomoya, kunye nokubala umgama phakathi kwabo okanye ukuzoba iigrafu zemisebenzi. Olu lwazi lusisiseko luya kuvula iingcango kwihlabathi lamathuba okufunda kunye nobungcali.

Kubalulekile ukukhumbula ukuba ulungelelwaniso kwinqwelomoya yeCartesian zihlala zifundwa ngokulandelelana (x, y), apho ulungelelwaniso lokuqala luhambelana nomgca we-x (othe tye) kwaye ulungelelwaniso lwesibini luhambelana nomgca we-y (othe nkqo). Ukongezelela, kuyimfuneko ukuqwalasela ukuba iiyunithi zokulinganisa kwi-axis nganye kufuneka zicace kwaye zihambelane nokutolikwa ngokuchanekileyo kwezilungelelaniso.

Isishwankathelo, ukuqonda indlela yokufunda ulungelelwaniso kwinqwelomoya yeCartesian yintsika esisiseko kuphuhliso lwezakhono zemathematika kunye nesithuba. Ngokuyilawula kakuhle le ngcamango, siya kukwazi ukunxibelelana ngokufanelekileyo sisebenzisa ulwimi lwendawo kunye nendawo kwinqwelomoya, ngaloo ndlela siququzelela umsebenzi wethu ekusombululeni iingxaki nasekumeleni idatha. Njengamaxesha onke, ukuziqhelanisa rhoqo kunye nokusetyenziswa kwezixhobo zobuchwepheshe ezikhoyo kuya kusivumela ukuba someleze izakhono zethu kule ntsimi kwaye sifezekise ukuqonda okupheleleyo kokutolika kunye nokusetyenziswa kolungelelwaniso kwinqwelomoya yeCartesian.