Tusaalooyin Dhibaatooyinka Ka Hadlaya Wareegga Xisaabta
Pendahuluan
Wareeggu waa isbeddel joomatari oo inta badan lagu arko xisaabta, gaar ahaan joomatari. Wareeggu wuxuu ku lug leeyahay wareejinta shay ku wareegsan meel gaar ah (xarunta wareegga) iyada oo loo marayo xagal gaar ah jihada saacadda ama ka soo horjeedda saacadda. Adeegsiga fikradda wareegga waa mid muhiim u ah meelaha sida sawirada kombiyuutarka, fiisigiska, iyo injineernimada. Maqaalkani wuxuu sahamin doonaa tusaalooyin iyo doodo kala duwan oo ku saabsan wareegga xisaabta.
Fahmidda Wareegga
Wareeggu waa isbeddel dhaqaajiya dhibic kasta oo shay ah isagoo ku wareejinaya meel go'an, oo loo yaqaan xarunta wareegga, iyadoo la adeegsanayo xagal gaar ah oo jiho gaar ah u socota. Calaamadda guud ee wareegga leh xagal θ iyo xarunta wareegga (a, b) waxaa loo qori karaa R_(a, b)(θ).
Barta P(x, y) ee lagu wareejiyo darajo θ oo leh bartamaha wareegga asalka (0, 0), isku-duwayaasha cusub ee P' (x', y') ka dib wareegga waxaa la heli doonaa iyadoo la adeegsanayo qaacidada:
– x' = x cos θ – y dembi θ
– y' = x sin θ + y cos θ
Aan sii wadno tusaalooyin ku saabsan dhibaatooyinka wareegga oo dhammaystiran dooddooda.
Su'aalo iyo Doodo Tusaale ah
Su'aal Tusaale 1aad
Su'aal: Go'aami isku-duwayaasha cusub ee dhibicda A(3, 4) ka dib markaad u rogto 90 darajo dhanka saacadda ka soo horjeedda iyadoo bartamaha wareegga uu ku yaal asalka (0, 0).
Dood: Iyada oo la adeegsanayo qaacidada wareegga oo leh xagal 90 darajo ah oo ka soo horjeeda saacadda:
– x' = x cos(90°) – y sin(90°) = 3(0) – 4(1) = -4
– y' = x dembi(90°) + y cos(90°) = 3(1) + 4(0) = 3
Markaa, isku-duwayaasha cusub ee A' ka dib wareegga waa (-4, 3).
Su'aal Tusaale 2aad
Su'aal: Barta B(2, -1) waxaa loo wareejiyaa 180 darajo jihada saacadda iyadoo bartamaha wareegga uu ku harsan yahay asalka (0, 0). Go'aami isku-duwayaasha cusub ee barta B ka dib wareegga.
Dood: Wareegga 180 digrii ee saacadda u jeeda ama ka soo horjeedka saacadda ayaa bixiya natiijo isku mid ah, taas oo ah isku-duwayaasha isbeddelka barta ilaa (-x, -y).
– x' = -x = -2
– y' = -y = 1
Markaa, isku-duwayaasha cusub ee B' waa (-2, 1).
Su'aal Tusaale 3aad
Su'aal: Barta C(-3, 5) waxaa loo rogaa 270 darajo dhanka saacadda ka soo horjeeda iyadoo bartamaha wareegga uu ku yaal asalka (0, 0). Go'aami barta C ka dib wareegga.
Dood: Wareeg 270 digrii ah oo ka soo horjeeda saacadda ayaa la mid ah wareeg 90 digrii ah oo saacadda u jeeda.
– x' = x cos(90°) + y dembi(90°) = -3(0) + 5(1) = 5
– y' = -x dembi(90°) + y cos(90°) = -(-3)(1) + 5(0) = 3
Markaa, isku-duwayaasha cusub ee C' ka dib wareegga waa (5, -3).
Su'aal Tusaale 4aad
Su'aal: Go'aami isku-duwayaasha cusub ee dhibicda D(5, 5) ka dib markaad ku wareejiso 45 darajo iyadoo bartamaha wareegga uu ku yaal asalka (0, 0).
Dood: Iyada oo la adeegsanayo qaacidada wareegga oo leh xagal 45 darajo ah:
– x' = x cos(45°) – y sin(45°) = 5(cos(45°)) – 5(denbi(45°)) = 5(√2/2) – 5(√2/2) = 0
– y' = x dembi (45°) + y cos(45°) = 5(√2/2) + 5(√2/2) = 5√2/2 + 5√2/2 = 5√2
Markaa, isku-duwayaasha cusub ee D' ka dib wareegga waa (0, 5√2).
Wareegga oo leh Xarunta Wareegga oo aan asal ahaan ahayn
Wareegyada had iyo jeer laguma sameeyo asalka. Tusaale ahaan, bal aan rabno inaan ku wareejino bar leh bartamaha wareegga (h, k). Si tan loo sameeyo, waxaan u baahanahay inaan isku-duwayaasha u hagaajinno sidan soo socota:
1. Turjum qodobka si (h, k) uu u noqdo asalka.
2. Isticmaal qaacidada wareegga.
3. Dib ugu turjun meeshii asalka ahayd.
Su'aal Tusaale 5aad
Su'aal: Barta E(5, 7) waxaa loo wareejiyaa 90 darajo dhanka saacadda ka soo horjeeda iyadoo bartamaha wareegga uu ku yaal barta (2, 3). Go'aami isku-duwayaasha cusub ee barta E ka dib wareegga.
Dood:
1. U turjun barta E asalka marka loo eego bartamaha wareegga (2, 3):
– Dhibco cusub E' = (5 – 2, 7 – 3) = (3, 4)
2. U wareeji 90 darajo dhanka saacadda ka soo horjeeda barta cusub:
– x' = 3 cos(90°) – 4 dembi(90°) = -4
- y' = 3 dembi (90°) + 4 cos(90°) = 3
Markaa, isku-duwayaasha wareegga ka dib waa (-4, 3).
3. Turjumaadda dib ugu noqo meeshii asalka ahayd marka loo eego bartamaha wareegga (2, 3):
– Dhibcaha ugu dambeeya E' = (-4 + 2, 3 + 3) = (-2, 6)
Markaa, isku-duwayaasha cusub ee dhibicda E ka dib wareegga waa (-2, 6).
Gabagabo
Falanqaynta iyo fahamka wareegyada xisaabeed waa muhiim marka la eego codsiyada kala duwan. Iyada oo loo marayo tusaalooyinka iyo doodaha kor ku xusan, akhristayaasha waxaa laga filayaa inay fahmaan sida qaacidooyinka wareeggu u shaqeeyaan iyo sida loogu dabaqi karo xaaladaha kala duwan. Layligani ma aha oo kaliya inuu xoojiyo xisaabta aasaasiga ah laakiin sidoo kale waa mid faa'iido leh meelaha kale ee ku lug leh isbeddellada joomatari.
