Izibonelo Zemibuzo Nezingxoxo Zokuhumusha Ngezibalo
Ukuhumusha kuwukuguqulwa kwejiyometri okuhambisa iphuzu ngalinye endizeni ibanga elithile endaweni ethile. Kumathematika, ukuhumusha kuvame ukusetshenziselwa ukuhambisa into endaweni eyodwa ngaphandle kokushintsha isimo sayo noma ukuma kwayo. Kulesi sihloko, sizoxoxa ngezinkinga eziningana zezibonelo kanye nezingxoxo ezihlobene nokuhumusha kwezibalo ukusiza abafundi baqonde kangcono lo mqondo.
Imiqondo Eyisisekelo Yokuhumusha
Ukuhumusha ngama-coordinates anezinhlangothi ezimbili kungavezwa kusetshenziswa i-vector notation. Uma iphuzu A(x, y) lihunyushwa yi-vector \((a, b)\), khona-ke iphuzu eliphumela ku-A' (\(x'\), \(y'\)) lingabalwa kusetshenziswa ifomula:
\[ x' = x + a \]
\[ y' = y + b \]
Kuphi:
– \( (x, y) \) yi-coordinate yokuqala,
– \( (a, b) \) iyivektha yokuhumusha,
– \( (x', y') \) yizixhumanisi zomphumela wokuhumusha.
Imibuzo Eyisibonelo Nengxoxo
Nazi ezinye izibonelo zemibuzo ephathelene nokuhumusha ngezibalo kanye nezingxoxo zazo:
Isibonelo Sombuzo 1:
Umbuzo:
Iphuzu A likuma-coordinates (3, 4). Humusha iphuzu A nge-vector \( (5, -2) \). Thola ama-coordinates amasha ephuzu A.
Ingxoxo:
Kuyaziwa:
\[ \text{Izixhumanisi zokuqala zephuzu A} = (3, 4) \]
\[ \umbhalo{Ivektha yokuhumusha} = (5, -2) \]
Sebenzisa ifomula yokuhumusha:
\[ x' = x + a \]
\[ y' = y + b \]
Faka amanani esikhundleni sawo:
\[x' = 3 + 5 = 8 \]
\[ y' = 4 + (-2) = 2 \]
Ngakho-ke, izixhumanisi ezintsha zephuzu A ngemuva kokuhumusha ziyi- \( (8, 2) \).
Isibonelo Sombuzo 2:
Umbuzo:
Unxantathu unezixhumanisi ze-vertex \( A(1, 2) \), \( B(3, 5) \), kanye \( C(6, 1) \). Humusha unxantathu nge-vector \( (-2, 4) \). Thola izixhumanisi ze-vertex zenxantathu ngemva kokuhumusha.
Ingxoxo:
Izixhumanisi ze-vertex yonxantathu kanye ne-vector yokuhumusha ziyaziwa.
Ama-Coordinates ephuzu A':
\[ x' = 1 + (-2) = -1 \]
\[y' = 2 + 4 = 6 \]
Bese kuthi, \( A' = (-1, 6) \).
Ama-Coordinates ephuzu B':
\[ x' = 3 + (-2) = 1 \]
\[y' = 5 + 4 = 9 \]
Bese kuthi, \( B' = (1, 9) \).
Ama-Coordinates ephuzu C':
\[ x' = 6 + (-2) = 4 \]
\[y' = 1 + 4 = 5 \]
Bese kuthi, \( C' = (4, 5) \).
Ngakho-ke, ngemva kokuhumusha, izixhumanisi zama-vertices onxantathu omusha yi-\( A'(-1, 6) \), \( B'(1, 9) \), kanye ne-\( C'(4, 5) \).
Isibonelo Sombuzo 3:
Umbuzo:
Iphuzu elinikeziwe P kuma-coordinates \( (-3, 0) \). Nquma umphumela wokuhunyushwa kwephuzu P ngevektha \( (7, -5) \).
Ingxoxo:
Njengoba kunikezwe izixhumanisi ze-P kanye nevektha yokuhumusha.
Sebenzisa ifomula yokuhumusha:
\[ x' = x + a \]
\[ y' = y + b \]
Faka amanani esikhundleni sawo:
\[ x' = -3 + 7 = 4 \]
\[ y' = 0 + (-5) = -5 \]
Ngakho-ke, izixhumanisi zomphumela wokuhumusha wephuzu P ziyi- \( (4, -5) \).
Isibonelo Sombuzo 4:
Umbuzo:
Iphuzu Q litholakala kuma-coordinates \( (4, -3) \). Uma iphuzu Q lihunyushwa ukuze ama-coordinates amasha abe \( (9, 1) \), nquma i-vector yokuhumusha esetshenzisiwe.
Ingxoxo:
Kuyaziwa:
\[ \text{Izixhumanisi zokuqala} = (4, -3) \]
\[ \umbhalo{Izixhumanisi zemiphumela} = (9, 1) \]
Sebenzisa ifomula yokuhumusha ukuthola i-vector \( (a, b) \):
\[ x' = x + a \]
\[ y' = y + b \]
Imiphumela yokuhumusha iyaziwa:
\[ 9 = 4 + a \]
\[ 1 = -3 + b \]
Ngakho-ke, i-vector yokuhumusha ingabalwa kanje:
\[ a = 9 – 4 = 5 \]
\[b = 1 + 3 = 4 \]
Ngakho-ke, ivektha yokuhumusha esetshenzisiwe yi-\( (5, 4) \).
Isibonelo Sombuzo 5:
Umbuzo:
I-quadrilateral ABCD inama-corner points \( A(1, 2) \), \( B(1, 5) \), \( C(4, 5) \), kanye \( D(4, 2) \). Humusha i-quadrilateral nge-vector \( (3, -1) \). Thola ama-coordinates amasha e-quadrilateral ABCD.
Ingxoxo:
Kuyaziwa:
\[ \umbhalo{Ivektha yokuhumusha} = (3, -1) \]
Ama-Coordinates ephuzu A':
\[x' = 1 + 3 = 4 \]
\[ y' = 2 + (-1) = 1 \]
Bese kuthi, \( A' = (4, 1) \).
Ama-Coordinates ephuzu B':
\[x' = 1 + 3 = 4 \]
\[ y' = 5 + (-1) = 4 \]
Bese kuthi, \( B' = (4, 4) \).
Ama-Coordinates ephuzu C':
\[x' = 4 + 3 = 7 \]
\[ y' = 5 + (-1) = 4 \]
Bese kuthi, \( C' = (7, 4) \).
Ama-Coordinates ephuzu D':
\[x' = 4 + 3 = 7 \]
\[ y' = 2 + (-1) = 1 \]
Bese kuthi, \( D' = (7, 1) \).
Ngakho-ke, ama-coordinates amasha e-quadrilateral ABCD ngemuva kokuhumusha yi-\( A'(4, 1) \), \( B'(4, 4) \), \( C'(7, 4) \), kanye ne-\( D'(7, 1) \).
Isiphetho
Ukuhumusha kuyindlela eyisisekelo kakhulu kodwa ebalulekile yokuguqula i-geometry. Ukwazi kahle le ndlela kusenza sikwazi ukwenza imisebenzi ehlukahlukene ye-geometry, njengokushintsha izinto ngaphandle kokushintsha isimo noma usayizi wazo.
Ngokuqonda umqondo wokuhumusha ngezinkinga ezahlukahlukene zezibonelo okuxoxwe ngazo ngenhla, kunethemba lokuthi abafundi bazokwazi ukuqonda kangcono nokusebenzisa lo mqondo ezinkingeni ezahlukahlukene nasempilweni yangempela. Ukuhumusha akusizi kuphela ezibalweni kodwa nakweminye imikhakha ehlukahlukene, okuhlanganisa i-physics, ihluzo zekhompyutha, kanye nokuklama.
