Ihe atụ nke Ajụjụ na Mkparịta ụka gbasara Mgbanwe Geometric
Mgbanwe Geometric bụ isiokwu dị mkpa na mgbakọ na mwepụ, nke a na-ejikarị eme ihe n'ọtụtụ ngalaba dịka fiziki, eserese kọmputa, na injinia. Mgbanwe Geometric gụnyere ọtụtụ ọrụ ndị na-agbanwe ọnọdụ, nha, na ntụzịaka nke ihe dị na mbara igwe. Ụfọdụ n'ime ụdị mgbanwe ndị bụ isi gụnyere ntụgharị, ntụgharị uche, ntụgharị, na mgbasa. Isiokwu a ga-ekpuchi ọtụtụ nsogbu atụ ma nye nkọwa miri emi gbasara mgbanwe geometric.
1. Nsụgharị
Ajụjụ:
Isi ihe A(2, 3) enyere. Mee ntụgharị asụsụ ka isi ihe A wee gaa na nhazi ọhụrụ. Nsụgharị a rụrụ bụ:
– nkeji ise n'aka nri
– nkeji 4 na karịa
Azịza:
Nsụgharị na-agbanwe isi ihe dị ka otu axis nhazi n'enweghị mgbanwe ọdịdị na nha nke ihe ahụ. Nsụgharị nke isi ihe (x, y) site na otu gaa n'aka nri na nkeji b elu nwere ike ịkọwa dị ka (x + a, y + b).
A maara na isi ihe A(2, 3) ga-asụgharị:
– nkeji ise n'aka nri pụtara +5 na axis x
– nkeji 4 elu pụtara +4 na y-axis
Nhazi ọhụrụ nke isi ihe A bụ:
\[ (2 + 5, 3 + 4) = (7, 7) \]
Ya mere, mgbe a tụgharịrị ya, isi ihe A dị na nhazi (7, 7).
2. Ntụgharị uche
Ajụjụ:
Ntụgharị uche nke isi ihe B(4, 5) gbasara y-axis.
Azịza:
Ntụgharị uche gbasara axis y ga-agbanwe nhazi x nke isi ihe ahụ gaa na uru adịghị mma ya, ebe nhazi y ka bụ otu ihe ahụ:
\[ B(x, y) \akara aka nri B'(-x, y) \]
Maka isi ihe B(4, 5), ntụgharị uche gbasara y-axis na-apụta:
\[ (-4, 5) \]
Ya mere, isi ihe B mgbe ntụgharị uche gbasara y-axis bụ (-4, 5).
3. Ntụgharị
Ajụjụ:
Mee ntụgharị nke ogo 90 n'akụkụ aka nri na isi C(1, 2) gbasara mmalite (0, 0).
Azịza:
Enwere ike igosi ntụgharị nke ogo 90 n'akụkụ aka nri site na mgbanwe nhazi ndị a:
\[ (x, y) \akara aka nri (y, -x) \]
Maka isi ihe C(1, 2), mgbe ntụgharị ogo 90 gasịrị:
\[ (1, 2) \akara aka nri (2, -1) \]
Ya mere, isi ihe C mgbe ntụgharị nke ogo 90 gasịrị n'akụkụ aka nri bụ (2, -1).
4. Mgbasa (Ịgbasa)
Ajụjụ:
A na-eme ka isi ihe D(3, 4) gbasaa site na nha nha nke 2 gbasara ebe etiti (0, 0).
Azịza:
Ịgbasa site na ihe nha k gbasara ebe etiti (0, 0) ga-agbanwe nhazi nke ebe (x, y) ka ọ bụrụ (kx, ky).
Maka isi ihe D(3, 4) na ihe nke abụọ n'ihe gbasara nha:
\[ (3, 4) \rightarrow (2 \ugboro 3, 2 \ugboro 4) = (6, 8) \]
Ya mere, isi ihe D mgbe e mechara gbasaa site na ihe nke abụọ bụ (6, 8).
5. Nhazi Mgbanwe
Ajụjụ:
Isi E(2, 3) na-apụta ìhè na mbụ gbasara x-axis, mgbe ahụ a ga-atụgharị nsonaazụ ya nkeji atọ gaa n'aka ekpe na otu nkeji ala.
Azịza:
Nzọụkwụ 1: Ntụgharị uche gbasara x-axis
Ntụgharị uche gbasara xe-x na-agbanwe y gaa na negative ya, ebe x ka bụ otu ihe ahụ:
\[ (x, y) \rightarrow (x, -y) \]
Maka isi ihe E(2, 3):
\[ (2, 3) \akara aka nri (2, -3) \]
Nzọụkwụ nke 2: Tụgharịa nkeji atọ gaa n'aka ekpe na otu nkeji ala
Enwere ike ịkọwa ntụgharị a dịka (x – 3, y – 1).
Maka isi ihe (2, -3), nsụgharị a na-enye:
\[ (2 – 3, -3 – 1) = (-1, -4) \]
Ya mere, isi ihe E mgbe a tụlechara anya gbasara x-axis na ntụgharị bụ (-1, -4).
6. Ntụgharị uche n'ahịrị y = x
Ajụjụ:
A na-egosipụta isi ihe F(5, 2) n'ofe ahịrị y = x.
Azịza:
Ntụgharị uche gbasara ahịrị y = x ga-agbanwe nhazi x na y nke isi ihe ahụ:
\[ (x, y) \akara aka nri (y, x) \]
Maka isi ihe F(5, 2):
\[ (5, 2) \akara aka nri (2, 5) \]
Ya mere, isi ihe F mgbe a tụlechara ahịrị y = x bụ (2, 5).
7. Mgbanwe Agwakọtara agwakọta
Ajụjụ:
Isi G(1, -2) na-eme njikọta mgbanwe ndị a:
1. Tụgharịa ogo 90 n'akụkụ aka ekpe gburugburu etiti (0, 0)
2. Mgbasawanye nke ihe nha nke 3 gbasara etiti (0, 0)
Azịza:
Nzọụkwụ 1: Tụgharịa ogo 90 n'akụkụ aka ekpe
Mgbanwe ahụ nwere ike igosi ntụgharị nke ogo 90 n'akụkụ aka nri site na mgbanwe ahụ:
\[ (x, y) \akara aka nri (-y, x) \]
Maka isi ihe G(1, -2):
\[ (1, -2) \akara aka nri (2, 1) \]
Nzọụkwụ nke 2: Mee ka ihe nha nke 3 gbasaa
Mgbasa nke ihe nha nha nke ihe dị ka 3 (0, 0):
\[ (x, y) \akara aka nri (3x, 3y) \]
Maka isi ihe (2, 1):
\[ (2, 1) \akara aka nri (6, 3) \]
Ya mere, isi ihe G mgbe njikọta nke mgbanwe gasịrị bụ (6, 3).
Mmechi
Mgbanwe Geometric bụ echiche dị mkpa nke gụnyere ntụgharị asụsụ, ntụgharị uche, ntụgharị uche, na mgbasa. Site na ihe atụ na mkparịta ụka dị n'elu, anyị nwere ike ịhụ otu ụdị mgbanwe ọ bụla si arụ ọrụ na otu esi ejikọta ha iji mepụta mmetụta dị mgbagwoju anya karịa na ihe geometric. Nghọta dị mma nke mgbanwe geometric ga-enyere aka nke ukwuu n'idozi nsogbu mgbakọ na mwepụ dị iche iche na ojiji ha n'ọtụtụ ngalaba sayensị.
