Mienzaniso yeMibvunzo neKukurukurirana pamusoro peKuchinja kweGeometric
Kuchinja kwejiyometri inyaya inokosha mumasvomhu, inoshandiswa zvakanyanya muzvikamu zvakasiyana-siyana zvakaita sefizikisi, mifananidzo yemakombiyuta, uye mainjiniya. Kuchinja kwejiyometri kunosanganisira mabasa akasiyana-siyana anochinja nzvimbo, saizi, uye kurongeka kwezvinhu zviri muchadenga. Mamwe emhando huru dzekuchinja anosanganisira kushandura, kufungisisa, kutenderera, uye kuwedzera. Chinyorwa chino chichakurukura matambudziko akati wandei uye kupa hurukuro yakadzama yekuchinja kwejiyometri.
1. Shanduro
Mubvunzo:
Kana wapiwa poindi A(2, 3). Ita shanduro kuitira kuti poindi A iende kune macoordinates matsva. Shanduro yakaitwa ndeiyi:
- mayuniti mashanu kurudyi
- mayuniti mana zvichikwira
Kukurukurirana:
Dudziro inoshandura poindi yakafanana neakisi ye coordinate pasina kuchinja chimiro nehukuru hwechinhu chacho. Dudziro yepoindi (x, y) neyuniti kurudyi uye b units kumusoro inogona kuratidzwa se (x + a, y + b).
Zvinozivikanwa kuti point A(2, 3) ichashandurwa:
- mayuniti mashanu kurudyi zvinoreva +5 pa x-axis
- 4 mayuniti kumusoro zvinoreva +4 pa y-axis
Makorodheni matsva epoindi A ndeaya:
\[ (2 + 5, 3 + 4) = (7, 7) \]
Saka, mushure mekushandura, poindi A iri pamakoneti (7, 7).
2. Kufungisisa
Mubvunzo:
Kufungisisa kwepoindi B(4, 5) nezve y-axis.
Kukurukurirana:
Kufungisisa nezve y-axis kuchachinja x-coordinate yepoindi kuita negative value yayo, nepo y-coordinate ichiramba yakafanana:
\[ B(x, y) \museve wekurudyi B'(-x, y) \]
Papfungwa B(4, 5), kufungisisa nezve y-axis goho:
\[ (-4, 5) \]
Saka, poindi B mushure mekufungisisa nezve y-axis ndeye (-4, 5).
3. Kutenderera
Mubvunzo:
Ita kutenderera kwemadhigirii makumi mapfumbamwe nemana uchitenderera wachi panzvimbo C(1, 2) maererano nekwakabva (0, 0).
Kukurukurirana:
Kutenderera kwe 90 degrees ne watchwide kunogona kuratidzwa nekuchinja kunotevera kwe coordinate:
\[ (x, y) \museve wekurudyi (y, -x) \]
Kune poindi C(1, 2), mushure mekutenderera kwemadhigirii makumi mapfumbamwe:
\[ (1, 2) \museve wekurudyi (2, -1) \]
Saka, poindi C mushure mekutenderera kwemadhigirii 90 newachi ndiyo (2, -1).
4. Kukura (Kuwedzera)
Mubvunzo:
Point D(3, 4) inowedzerwa nescale factor ye2 pamusoro pepoint yepakati (0, 0).
Kukurukurirana:
Kuwedzerwa nechiyero k pamusoro penzvimbo yepakati (0, 0) kuchachinja ma coordinates enzvimbo (x, y) kuita (kx, ky).
Kune poindi D(3, 4) uye chiyero 2:
\[ (3, 4) \museve wekurudyi (2 \kawa 3, 2 \kawa 4) = (6, 8) \]
Saka, poindi D mushure mekuwedzerwa ne factor ye2 ndiyo (6, 8).
5. Kuumbwa kweShanduko
Mubvunzo:
Poindi E(2, 3) inotanga kuratidzwa pamusoro pe x-axis, zvino mhedzisiro yacho inoshandurwa mayuniti matatu kuruboshwe uye yuniti imwe pasi.
Kukurukurirana:
Danho 1: Kufungisisa nezve x-axis
Kufungisisa nezve x-axis kunochinja y kuita negative, nepo x ichiramba yakafanana:
\[ (x, y) \museve wekurudyi (x, -y) \]
Kune poindi E(2, 3):
\[ (2, 3) \museve wekurudyi (2, -3) \]
Danho rechipiri: Shandura mayuniti matatu kuruboshwe uye 1 pasi
Dudziro iyi inogona kutsanangurwa se (x - 3, y - 1).
Panyaya iyi (2, -3), shanduro iyi inopa:
\[(2 – 3, -3 – 1) = (-1, -4) \]
Saka, poindi E mushure mekufungisisa nezve x-axis uye shanduro ndeye (-1, -4).
6. Kufungisisa pamutsetse y = x
Mubvunzo:
Poindi F(5, 2) inoratidzwa pamutsetse we y = x.
Kukurukurirana:
Kufungisisa nezvemutsara we y = x kuchachinjana ma coordinates e x ne y epoindi:
\[ (x, y) \museve wekurudyi (y, x) \]
Panyaya F(5, 2):
\[ (5, 2) \museve wekurudyi (2, 5) \]
Saka, poindi F mushure mekufungisisa nezvemutsetse y = x ndiyo (2, 5).
7. Kuchinja Kwakabatana
Mubvunzo:
Poindi G(1, -2) inosangana nemusanganiswa wekushandurwa kunotevera:
1. Tenderedza madhigirii 90 uchitenderedza pakati (0, 0)
2. Kukura kwechikamu chepakati (0, 0) nechikamu chepakati (scale factor) che3.
Kukurukurirana:
Danho 1: Tenderedza madhigirii 90 uchipesana newachi
Kutenderera kwemadhigirii makumi mapfumbamwe nemana kunodzorwa newachi kunogona kuratidzwa nekushandurwa:
\[ (x, y) \museve wekurudyi (-y, x) \]
Kune poindi G(1, -2):
\[ (1, -2) \museve wekurudyi (2, 1) \]
Danho rechipiri: Wedzera nechiyero che3
Kukura kwechikamu nechiyero che3 nezve (0, 0):
\[ (x, y) \museve wekurudyi (3x, 3y) \]
Kuti uwane pfungwa (2, 1):
\[ (2, 1) \museve wekurudyi (6, 3) \]
Saka, poindi G mushure mekusanganiswa kweshanduko ndeye (6, 3).
Mhedziso
Kuchinja kwejiyometri ipfungwa dzakakosha dzinosanganisira kushandurwa, kufungisisa, kutenderera, uye kuwedzera. Kuburikidza nemienzaniso nehurukuro dziri pamusoro apa, tinogona kuona kuti rudzi rumwe nerumwe rwekuchinja runoshanda sei uye kuti runogona sei kubatanidzwa kuti rugadzire mhedzisiro yakaoma pazvinhu zvejiyometri. Kunzwisisa kwakanaka kwekuchinja kwejiyometri kuchabatsira zvikuru mukugadzirisa matambudziko akasiyana-siyana emasvomhu uye mashandisirwo awo muminda yakasiyana-siyana yesainzi.
