Izibonelo Zezinkinga Zokuxoxa Ngokuzungeza Kwezibalo
I-Pendahuluan
Ukujikeleza kuyinguquko yejiyometri evame ukuhlangana nayo ezibalweni, ikakhulukazi ijiyometri. Ukujikeleza kuhilela ukujikeleza into izungeze iphuzu elithile (isikhungo sokujikeleza) nge-engeli ethile ngendlela yewashi noma ephambene newashi. Ukusetshenziswa komqondo wokujikeleza kubalulekile emikhakheni efana nezithombe zekhompyutha, i-physics, kanye nobunjiniyela. Lesi sihloko sizohlola izibonelo ezahlukahlukene kanye nezingxoxo zokujikeleza ezibalweni.
Ukuqonda Ukuzungeza
Ukujikeleza kungukuguqulwa okuhambisa yonke indawo yento ngokuyijikeleza cishe endaweni ethile, ebizwa ngokuthi isikhungo sokujikeleza, nge-engeli ethile ohlangothini oluthile. Umbhalo ojwayelekile wokujikeleza one-engeli engu-θ kanye nesikhungo sokujikeleza (a, b) ungabhalwa njengo-R_(a, b)(θ).
Ukuze uthole iphuzu elithi P(x, y) elijikelezwe ngama-θ degrees kanye nesikhungo sokujikeleza ekuqaleni (0, 0), izixhumanisi ezintsha ze-P' (x', y') ngemva kokujikeleza zizotholakala kusetshenziswa ifomula:
– x' = x cos θ – y isono θ
– y' = x sin θ + y cos θ
Ake siqhubeke nezibonelo zezinkinga zokujikeleza ezipheleliswa yizingxoxo zazo.
Imibuzo Eyisibonelo Nengxoxo
Isibonelo Umbuzo 1
Umbuzo: Thola ama-coordinates amasha ephuzu A(3, 4) ngemva kokulizungezisa ngama-degree angu-90 ngokuphambene newashi nendawo ephakathi nendawo lapho kuqale khona (0, 0).
Ingxoxo: Ukusebenzisa ifomula yokujikeleza nge-engeli engama-degree angu-90 ephambene newashi:
– x' = x cos(90°) – y isono(90°) = 3(0) – 4(1) = -4
– y' = x isono(90°) + y cos(90°) = 3(1) + 4(0) = 3
Ngakho-ke, ama-coordinates amasha e-A' ngemva kokujikeleza angu-(-4, 3).
Isibonelo Umbuzo 2
Umbuzo: Iphuzu B(2, -1) lijikeleziswa ngamadigri ayi-180 ngendlela yewashi kanti isikhungo sokujikeleza sisele ekuqaleni (0, 0). Thola ama-coordinates amasha ephuzu B ngemva kokujikeleza.
Ingxoxo: Ukujikeleza kwama-degree angu-180 kungaba ngokwewashi noma ngokuphambene newashi kunikeza umphumela ofanayo, okungukuthi ama-coordinates ephuzu ashintshela ku-(-x, -y).
– x' = -x = -2
– y' = -y = 1
Ngakho-ke, izixhumanisi ezintsha ze-B' ziyi-(-2, 1).
Isibonelo Umbuzo 3
Umbuzo: Iphuzu C(-3, 5) lijikeleziswa ngamadigri angu-270 ngokuphambene newashi lapho isikhungo sokujikeleza siqala khona (0, 0). Thola iphuzu C ngemva kokujikeleza.
Ingxoxo: Ukujikeleza okungamadigri angu-270 ngokuphambene newashi kufana nokujikeleza okungamadigri angu-90 ngokuhambisana newashi.
– x' = x cos(90°) + y isono(90°) = -3(0) + 5(1) = 5
– y' = -x isono(90°) + y cos(90°) = -(-3)(1) + 5(0) = 3
Ngakho-ke, ama-coordinates amasha ka-C' ngemva kokujikeleza angu-(5, -3).
Isibonelo Umbuzo 4
Umbuzo: Thola ama-coordinates amasha ephuzu D(5, 5) ngemva kokulizungeza ngama-degree angu-45 ngesikhungo sokujikeleza ekuqaleni (0, 0).
Ingxoxo: Ukusebenzisa ifomula yokujikeleza ene-engeli engama-degree angu-45:
– x' = x cos(45°) – y isono(45°) = 5(cos(45°)) – 5(isono(45°)) = 5(√2/2) – 5(√2/2) = 0
– y' = x isono(45°) + y cos(45°) = 5(√2/2) + 5(√2/2) = 5√2/2 + 5√2/2 = 5√2
Ngakho-ke, ama-coordinates amasha ka-D' ngemva kokujikeleza angu-(0, 5√2).
Ukujikeleza Ngesikhungo Sokujikeleza Akukhona Ekuqaleni
Ukuzungeza akwenziwa njalo mayelana nomsuka. Isibonelo, ake sithi sifuna ukuzungeza iphuzu elinendawo ephakathi yokuzungeza (h, k). Ukuze senze lokhu, sidinga ukulungisa ama-coordinates kanje:
1. Humusha iphuzu ukuze u-(h, k) abe umsuka.
2. Sebenzisa ifomula yokujikeleza.
3. Humusha ubuyele endaweni yokuqala.
Isibonelo Umbuzo 5
Umbuzo: Iphuzu E(5, 7) lijikeleziswa ngamadigri angu-90 ngokuphambene newashi lapho isikhungo sokujikeleza sisendaweni (2, 3). Thola ama-coordinates amasha ephuzu E ngemva kokujikeleza.
Ingxoxo:
1. Humusha iphuzu E libe yisiqalo maqondana nesikhungo sokujikeleza (2, 3):
– Iphuzu elisha E' = (5 – 2, 7 – 3) = (3, 4)
2. Jikelezisa amadigri angu-90 ngokuphambene newashi uzungeze iphuzu elisha:
– x' = 3 cos(90°) – 4 sin(90°) = -4
– y' = 3 isono(90°) + 4 cos(90°) = 3
Ngakho-ke, izixhumanisi ngemva kokujikeleza ziyi-(-4, 3).
3. Ukuhumusha emuva endaweni yokuqala maqondana nendawo ephakathi yokujikeleza (2, 3):
– Iphuzu lokugcina E' = (-4 + 2, 3 + 3) = (-2, 6)
Ngakho-ke, izixhumanisi ezintsha zephuzu E ngemva kokujikeleza ziyi-(-2, 6).
Isiphetho
Ukuhlaziya nokuqonda ukujikeleza kwezibalo kubalulekile ekusetshenzisweni okuhlukahlukene. Ngezibonelo nezingxoxo ezingenhla, abafundi kulindeleke ukuthi baqonde ukuthi amafomula okujikeleza asebenza kanjani nokuthi angasetshenziswa kanjani ezimweni ezahlukene. Lo msebenzi awugcini nje ngokuqinisa izibalo eziyisisekelo kodwa futhi uwusizo nakweminye imikhakha ehilela ukuguqulwa kwejiyometri.
