Mienzaniso yeMibvunzo neHurukuro dzeKushandura Masvomhu
Dudziro ishanduko yejometri inofambisa poindi yega yega mundege daro rakati rekuenda kune rimwe divi. Mumasvomhu, dudziro inowanzo shandiswa kufambisa chinhu kuenda kune rimwe divi pasina kushandura chimiro chayo kana kuti kwachinobva. Muchinyorwa chino, tichakurukura mienzaniso yakati wandei yezvinetso nehurukuro dzine chekuita nedudziro yemasvomhu kuti tibatsire vaverengi kunzwisisa zviri nani pfungwa iyi.
Pfungwa Dzekutanga dzeDudziro
Dudziro iri muzvikamu zviviri inogona kuratidzwa uchishandisa vector notation. Kana poindi A(x, y) yakashandurwa nevector \((a, b)\), ipapo poindi inobuda A' (\(x'\), \(y'\)) inogona kuverengerwa uchishandisa fomura:
\[ x' = x + a \]
\[ y' = y + b \]
Dimana:
– \( (x, y) \) ndiyo coordinate yekutanga,
– \( (a, b) \) ndiyo vhekitori yekushandura,
– \( (x', y') \) ndiwo marongero emhedzisiro yeshanduro.
Mibvunzo yemuenzaniso nekukurukurirana
Heano mimwe mienzaniso yemibvunzo ine chekuita neshanduro yemasvomhu nehurukuro dzayo:
Muenzaniso Mubvunzo 1:
Mubvunzo:
Poindi A iri pamakoneti (3, 4). Shandura poindi A uchishandisa vector \( (5, -2) \). Sarudza makoneti matsva epoindi A.
Kukurukurirana:
Zvinozivikanwa:
\[ \text{Makorodheni ekutanga epoindi A} = (3, 4) \]
\[ \text{Translation vector} = (5, -2) \]
Shandisa fomura yekushandura:
\[ x' = x + a \]
\[ y' = y + b \]
Tsiva tsika:
\[x' = 3 + 5 = 8 \]
\[ y' = 4 + (-2) = 2 \]
Saka, makoroneti matsva epoindi A mushure mekushandurwa ndeaya \( (8, 2) \).
Muenzaniso Mubvunzo 2:
Mubvunzo:
Katatu ine ma "vertex coordinates" \( A(1, 2) \), \( B(3, 5) \), uye \( C(6, 1) \). Shandura katatu ne "vector" \( (-2, 4) \). Sarudza ma "vertex coordinates" e "triangle" mushure mekushandura.
Kukurukurirana:
Makorodheni e vertex yetriangle uye vhekitori yekushandura anozivikanwa.
Makorodheni epoindi A':
\[ x' = 1 + (-2) = -1 \]
\[ y' = 2 + 4 = 6 \]
Zvadaro, \( A' = (-1, 6) \).
Makorodheni epoindi B':
\[ x' = 3 + (-2) = 1 \]
\[ y' = 5 + 4 = 9 \]
Zvadaro, \( B' = (1, 9) \).
Makorodheni epoindi C':
\[ x' = 6 + (-2) = 4 \]
\[ y' = 1 + 4 = 5 \]
Zvadaro, \( C' = (4, 5) \).
Saka, mushure mekushandurwa, ma coordinates e vertices e triangle itsva ndeanoti \( A'(-1, 6) \), \( B'(1, 9) \), uye \( C'(4, 5) \).
Muenzaniso Mubvunzo 3:
Mubvunzo:
Yakapihwa poindi P pa coordinates \( (-3, 0) \). Sarudza mhedzisiro yekushandurwa kwepoindi P nevector \( (7, -5) \).
Kukurukurirana:
Zvichienderana nemakoordinates eP uye vhekitari yekushandura.
Shandisa fomura yekushandura:
\[ x' = x + a \]
\[ y' = y + b \]
Tsiva tsika:
\[ x' = -3 + 7 = 4 \]
\[ y' = 0 + (-5) = -5 \]
Saka, makoronesheni emhedzisiro yeshanduro yepoinzi P ndeaya \( (4, -5) \).
Muenzaniso Mubvunzo 4:
Mubvunzo:
Poindi Q iri pamakoneti \( (4, -3) \). Kana poindi Q yashandurwa kuitira kuti makoneti matsva ave \( (9, 1) \), sarudza vhekitari yekushandura yakashandiswa.
Kukurukurirana:
Zvinozivikanwa:
\[ \text{Makoronike ekutanga} = (4, -3) \]
\[ \text{Result coordinates} = (9, 1) \]
Shandisa fomura yekushandura kuti uwane vhekitari \( (a, b) \):
\[ x' = x + a \]
\[ y' = y + b \]
Mhedzisiro yeshanduro inozivikanwa:
\[ 9 = 4 + a \]
\[ 1 = -3 + b \]
Saka, vhekitari yekushandura inogona kuverengerwa seinotevera:
\[a = 9 – 4 = 5 \]
\[b = 1 + 3 = 4 \]
Saka, vhekitari yekushandura inoshandiswa ndi \( (5, 4) \).
Muenzaniso Mubvunzo 5:
Mubvunzo:
Quadrilateral ABCD ine macorner points \( A(1, 2) \), \( B(1, 5) \), \( C(4, 5) \), uye \( D(4, 2) \). Shandura quadrilateral nevector \( (3, -1) \). Sarudza macoordinates matsva equadrilateral ABCD.
Kukurukurirana:
Zvinozivikanwa:
\[ \text{Translation vector} = (3, -1) \]
Makorodheni epoindi A':
\[x' = 1 + 3 = 4 \]
\[ y' = 2 + (-1) = 1 \]
Zvadaro, \( A' = (4, 1) \).
Makorodheni epoindi B':
\[x' = 1 + 3 = 4 \]
\[ y' = 5 + (-1) = 4 \]
Zvadaro, \( B' = (4, 4) \).
Makorodheni epoindi C':
\[x' = 4 + 3 = 7 \]
\[ y' = 5 + (-1) = 4 \]
Zvadaro, \( C' = (7, 4) \).
Makorodheni epoindi D':
\[x' = 4 + 3 = 7 \]
\[ y' = 2 + (-1) = 1 \]
Zvadaro, \( D' = (7, 1) \).
Saka, macoordinates matsva equadrilateral ABCD mushure mekushandurwa ndeaya \( A'(4, 1) \), \( B'(4, 4) \), \( C'(7, 4) \), uye \( D'(7, 1) \).
Mhedziso
Kushandura ishanduko iri nyore asi yakakosha mu geometry. Kugona nzira iyi kunoita kuti tikwanise kuita mabasa akasiyana-siyana e geometry, akadai sekufambisa zvinhu pasina kuchinja chimiro chazvo kana saizi yazvo.
Nekunzwisisa pfungwa yekushandura kuburikidza nemuenzaniso wematambudziko akasiyana-siyana ataurwa pamusoro apa, zvinotarisirwa kuti vaverengi vachakwanisa kunzwisisa zviri nani nekushandisa pfungwa iyi mumatambudziko akasiyana-siyana uye muhupenyu chaihwo. Kushandura kunobatsira kwete mumasvomhu chete asiwo mune mamwe matimu akasiyana-siyana, anosanganisira fizikisi, mifananidzo yemakombiyuta, uye dhizaini.
