Muenzaniso weMibvunzo yeKukurukurirana kweMasvomhu
Kukura, kana kushanduka kunosanganisira kuwedzera nekuderedza, ipfungwa yakakosha mukuchinja kwechimiro. Pfungwa iyi inowanzoonekwa mumamiriro akasiyana-siyana, akadai sekudzidza mapatani, kuenzanisa, uye mamwe mashandisirwo akawanda ehupenyu chaihwo. Chinyorwa chino chichakurukura pfungwa yekukura mumasvomhu uye kupa mienzaniso yakati wandei yezvinetso nemhinduro.
Chii chinonzi Dilation?
Kukura kwechinhu (dilation) ishanduko yejometri inosanganisira kuwedzera kana kuderedza chifananidzo nechimwe chinhu chechiyero. Mukukura, poindi iri pamufananidzo wejometri inosuduruka kana kuswedera pedyo kubva pakati pepoindi yekukura kwechinhu nechinhu chimwe chete. Kukura kwechinhu kunogona kuwedzera (scale factor > 1), kuderedza (0 < scale factor < 1), kana kutoratidza chifananidzo kana chifananidzo chiri negative. Zvinyorwa muKukura Kwechinhu Pakuita kuwedzera kwechinhu, mamwe mashoko anowanzo shandiswa anosanganisira: - Pakati peKukura Kwechinhu (P): Poindi yakatarwa inoshandiswa sereferensi mukuita kwekuwedzera. - Scale Factor (k): Chiyero chehurefu chinosarudza kuti kukura kana kuderedza kwakawanda sei kunoitika. Kana \( k > 1 \), chinhu chichakudzwa. Kana \( 0 < k < 1 \), chinhu chichaderedzwa.
Ngatitii poindi A ine macoordinates (x, y) yakawedzerwa kusvika papoindi A' ine scale factor ya k uye pakati pedilation paO (0,0), ipapo macoordinates aA' ari (kx, ky). Dilation Formula Kuti uwane macoordinates matsva emhedzisiro yakaderedzwa yepoindi, fomura inoshandiswa ndeiyi: \[ A' = (x', y') = (kx, ky) \] apo (x, y) ari macoordinates ekutanga epoindi uye k ndiyo scale factor. Muenzaniso weMibvunzo neKukurukurirana Muenzaniso Mubvunzo 1 Poindi A (2, 3) yakawedzerwa nescale factor ya2 uye pakati pedilation iri paO (0, 0). Sarudza macoordinates epoindi A mushure medilation. Kukurukurirana: Macoordinates epoindi A ari (2, 3), scale factor ndi k = 2, uye pakati pedilation ndiO (0, 0). Zvichienderana nefomura yekudiridza: \[ A' = (kx, ky) = (2 \cdot 2, 2 \cdot 3) = (4, 6) \] Saka, macoordinates epoindi A mushure mekudiridza ndeaya (4, 6). Muenzaniso Mubvunzo 2 Poindi B (-1, 4) inodiridza nescale factor ye0,5 uye pakati pekudiridza paO (0, 0). Sarudza macoordinates epoindi B mushure mekudiridza. Mhinduro: Macoordinates epoindi B ndeaya (-1, 4), scale factor k = 0,5, uye pakati pekudiridza ipoindi O (0, 0). Zvichienderana nefomura yekudiridza: \[ B' = (kx, ky) = (0,5 \cdot -1, 0,5 \cdot 4) = (-0,5, 2) \] Saka, macoordinates epoindi B mushure mekuwedzerwa kwenhamba ari (-0,5, 2). Muenzaniso Mubvunzo 3 Poindi C (3, -2) yakatambanudzwa nechiyero che -1 uye pakati pekuwedzerwa kwenhamba iri paO (0, 0). Sarudza macoordinates epoindi C mushure mekuwedzerwa kwenhamba. Mhinduro: Macoordinates epoindi C ari (3, -2), chiyero che k = -1, uye pakati pekuwedzerwa kwenhamba iri papoindi O (0, 0). Zvichienderana nefomura yekuwedzerwa kwenhamba: \[ C' = (kx, ky) = (-1 \cdot 3, -1 \cdot -2) = (-3, 2) \] Saka, macoordinates epoindi C mushure mekuwedzerwa kwenhamba ari (-3, 2). Muenzaniso Mubvunzo 4 Poindi D (2, 5) yakatambanudzwa nechiyero che 3 uye pakati pekuwedzerwa kwenhamba iri paP (1, 1). Sarudza macoordinates epoindi D mushure mekuwedzerwa kwenhamba. Kukurukurirana: Makorodheni epoindi D ndeaya (2, 5), chikero chechiyero k = 3, uye pakati pekuwedzera ipoindi P (1, 1). Kutanga, tinochinja poindi D kuenda kuhurongwa hwekubatanidza hwepakati pekuwedzera P (1, 1): Makorodheni ehukama eD kuenda kuP ndeaya: \[ D_r = (2 - 1, 5 - 1) = (1, 4) \] Ita dilation ne scale factor k panzvimbo D_r: \[ D_r' = (kx, ky) = (3 \cdot 1, 3 \cdot 4) = (3, 12) \] Pakupedzisira, tinodzosera poindi D_r' kuhurongwa hwekutanga hwe coordinate: \[ D' = (D_r' + P) = (3 + 1, 12 + 1) = (4, 13) \] Saka, ma coordinate e poindi D mushure me dilation ndeaya (4, 13). Muenzaniso Mubvunzo 5 Poindi E (-2, -3) inowedzerwa ne scale factor ye 0,25 uye pakati pe dilation pa P (-1, -1). Sarudza ma coordinate e poindi E mushure me dilation. Mhinduro: Ma coordinate e poindi E ndeaya (-2, -3), scale factor k = 0,25, uye pakati pe dilation pa P (-1, -1). Kutanga, tinochinja poindi E kuenda kudilation centre coordinate system P (-1, -1): Ma coordinate e E kuenda ku P ndeaya: \[ E_r = (-2 - (-1), -3 - (-1)) = (-2 + 1, -3 + 1) = (-1, -2) \] Ita dilation ne scale factor k pane poindi E_r: \[ E_r' = (kx, ky) = (0,25 \cdot -1, 0,25 \cdot -2) = (-0,25, -0,5) \] Pakupedzisira, tinodzosera poindi E_r' kune system yekutanga coordinate: \[ E' = (E_r' + P) = (-0,25 - 1, -0,5 - 1) = (-1,25, -1,5) \] Saka, coordinate dzepoindi E mushure me dilation ndi (-1,25, -1,5). Mhedziso: Kukura kwechikamu (dilation) ishanduko yejometri iyo inowedzera kana kuderedza chimiro chejometri nechiyero chakati. Kunzwisisa pfungwa uye mashandisirwo ekukura kwechikamu kunobatsira zvikuru muzvikamu zvakasiyana-siyana zvekudzidza, kunyanya mujometri. Nemienzaniso nehurukuro, zvinotarisirwa kuti izvi zvichabatsira vadzidzi nevaverengi kunzwisisa zviri nani nekushandisa pfungwa yekukura kwechikamu mumamiriro akasiyana-siyana emasvomhu.