Izibonelo Zemibuzo Nezingxoxo Ngokuguqulwa Kwejiyometri
Ukuguqulwa kwejiyomethri kuyisihloko esibalulekile kwizibalo, esisetshenziswa kabanzi emikhakheni ehlukahlukene njengefiziksi, ihluzo zekhompyutha, kanye nobunjiniyela. Ukuguqulwa kwejiyomethri kuhlanganisa imisebenzi ehlukahlukene eshintsha indawo, usayizi, kanye nokuqondiswa kwezinto esikhaleni. Ezinye zezinhlobo eziyinhloko zokuguqulwa zifaka phakathi ukuhumusha, ukuzindla, ukujikeleza, kanye nokwanda. Lesi sihloko sizomboza izinkinga eziningana zezibonelo futhi sinikeze ingxoxo ejulile yokuguqulwa kwejiyomethri.
1. Ukuhumusha
Umbuzo:
Iphuzu elinikeziwe A(2, 3). Yenza ukuhumusha ukuze iphuzu A lithuthele kuma-coordinates amasha. Ukuhumusha okwenziwe yilokhu:
– amayunithi ama-5 ngakwesokudla
- amayunithi ama-4 nangaphezulu
Ingxoxo:
Ukuhumusha kushintsha iphuzu elihambisana ne-axis ethile yokuxhumanisa ngaphandle kokushintsha ukuma nosayizi wento. Ukuhumusha iphuzu (x, y) ngeyunithi ngakwesokudla kanye namayunithi b phezulu kungachazwa ngokuthi (x + a, y + b).
Kuyaziwa ukuthi iphuzu A(2, 3) lizohunyushwa ngokuthi:
– Amayunithi ama-5 ngakwesokudla asho +5 ku-x-axis
– Amayunithi angu-4 phezulu asho +4 ku-y-axis
Izixhumanisi ezintsha zephuzu A yilezi:
\[ (2 + 5, 3 + 4) = (7, 7) \]
Ngakho-ke, ngemva kokuhumusha, iphuzu A lisezinhlakeni (7, 7).
2. Ukuzindla
Umbuzo:
Ukuzindla kwephuzu B(4, 5) mayelana ne-y-axis.
Ingxoxo:
Ukuzindla nge-y-axis kuzoshintsha i-x-coordinate yephuzu ibe yinani layo elibi, kuyilapho i-y-coordinate ihlala ifana:
\[ B(x, y) \umcibisholo ongakwesokudla B'(-x, y) \]
Ngephuzu B(4, 5), ukuzindla mayelana nezithelo ze-y-axis:
\[ (-4, 5) \]
Ngakho-ke, iphuzu B ngemva kokuzindla nge-y-axis liyi-(-4, 5).
3. Ukujikeleza
Umbuzo:
Yenza ukujikeleza okungu-90 degrees ngokwewashi endaweni ethi C(1, 2) mayelana nomsuka (0, 0).
Ingxoxo:
Ukujikeleza kwewashi okungama-degree angu-90 kungabonakaliswa ngoshintsho olulandelayo lwe-coordinate:
\[ (x, y) \umcibisholo ongakwesokudla (y, -x) \]
Ngephuzu C(1, 2), ngemva kokujikeleza kwamadigri angu-90:
\[ (1, 2) \umcibisholo ongakwesokudla (2, -1) \]
Ngakho-ke, iphuzu C ngemva kokujikeleza kwamadigri angu-90 ngokwewashi lingu-(2, -1).
4. Ukwanda (Ukwanda)
Umbuzo:
Iphuzu D(3, 4) linwetshwa yisilinganiso esingu-2 mayelana nephuzu eliphakathi (0, 0).
Ingxoxo:
Ukwandiswa yi-scale factor k mayelana ne-center point (0, 0) kuzoshintsha ama-coordinates e-point (x, y) abe yi-(kx, ky).
Ngephuzu D(3, 4) kanye nesici sesikali 2:
\[ (3, 4) \umcibisholo ongakwesokudla (2 \izikhathi 3, 2 \izikhathi 4) = (6, 8) \]
Ngakho-ke, iphuzu D ngemva kokwandiswa nge-factor engu-2 lingu-(6, 8).
5. Ukwakheka Kokuguqulwa
Umbuzo:
Iphuzu E(2, 3) liqala ukubonakala mayelana ne-x-axis, bese umphumela uhunyushwa amayunithi ama-3 ngakwesobunxele kanye neyunithi eli-1 phansi.
Ingxoxo:
Isinyathelo 1: Ukuzindla nge-x-axis
Ukuzindla nge-x-axis kushintsha u-y abe yi-negative yayo, kuyilapho u-x ehlala efana:
\[ (x, y) \umcibisholo ongakwesokudla (x, -y) \]
Ngephuzu E(2, 3):
\[ (2, 3) \umcibisholo ongakwesokudla (2, -3) \]
Isinyathelo 2: Humusha amayunithi ama-3 ngakwesobunxele kanye neyunithi eli-1 phansi
Lokhu kuhumusha kungachazwa kanje (x – 3, y – 1).
Ngephuzu (2, -3), lokhu kuhumusha kuveza:
\[ (2 – 3, -3 – 1) = (-1, -4) \]
Ngakho-ke, iphuzu u-E ngemva kokuzindla nge-x-axis kanye nokuhumusha kungu-(-1, -4).
6. Ukuzindla emgqeni u-y = x
Umbuzo:
Iphuzu F(5, 2) libonakala kulo lonke umugqa u-y = x.
Ingxoxo:
Ukuzindla ngomugqa u-y = x kuzoshintshanisa izixhumanisi zika-x no-y zephuzu:
\[ (x, y) \umcibisholo ongakwesokudla (y, x) \]
Ngephuzu F(5, 2):
\[ (5, 2) \umcibisholo ongakwesokudla (2, 5) \]
Ngakho-ke, iphuzu F ngemva kokuzindla ngomugqa u-y = x ngu-(2, 5).
7. Ukuguqulwa Okuhlanganisiwe
Umbuzo:
Iphuzu G(1, -2) lidlula kule nhlanganisela elandelayo yokuguqulwa:
1. Phendukisa amadigri angu-90 ngokuphambene newashi phakathi nendawo (0, 0)
2. Ukwanda ngesilinganiso sesikali esingu-3 mayelana nendawo ephakathi (0, 0)
Ingxoxo:
Isinyathelo 1: Jikelezisa ama-degree angu-90 ngokuphambene newashi
Ukujikeleza okungama-degree angu-90 ngokuphambene newashi kungabonakaliswa ngokuguqulwa:
\[ (x, y) \umcibisholo ongakwesokudla (-y, x) \]
Ngephuzu G(1, -2):
\[ (1, -2) \umcibisholo ongakwesokudla (2, 1) \]
Isinyathelo 2: Yandisa ngesilinganiso esingu-3
Ukwanda ngesilinganiso sesikali esingu-3 cishe (0, 0):
\[ (x, y) \umcibisholo ongakwesokudla (3x, 3y) \]
Ngephuzu (2, 1):
\[ (2, 1) \umcibisholo ongakwesokudla (6, 3) \]
Ngakho-ke, iphuzu G ngemuva kokuhlanganiswa kokuguqulwa lingu-(6, 3).
Isiphetho
Ukuguqulwa kwejiyomethri kuyimiqondo ebalulekile ehlanganisa ukuhumusha, ukuzindla, ukujikeleza, kanye nokwanda. Ngezibonelo nezingxoxo ezingenhla, singabona ukuthi uhlobo ngalunye lokuguqulwa lusebenza kanjani nokuthi lungahlanganiswa kanjani ukuze kukhiqizwe imiphumela eyinkimbinkimbi kakhulu ezintweni zejiyomethri. Ukuqonda kahle ukuguqulwa kwejiyomethri kuzosiza kakhulu ekuxazululeni izinkinga ezahlukahlukene zezibalo kanye nokusetshenziswa kwazo emikhakheni eyahlukene yesayensi.
