Mehlala ea Lipotso le Lipuisano tsa Phetolelo ea Lipalo
Phetolelo ke phetoho ea jeometri e tsamaisang ntlha ka 'ngoe sefofaneng sebaka se itseng ka lehlakoreng le itseng. Lipalong, phetolelo hangata e sebelisoa ho suthisa ntho ka lehlakoreng le leng ntle le ho fetola sebopeho kapa tsela eo e shebaneng le eona. Sehloohong sena, re tla buisana ka mathata a 'maloa a mehlala le lipuisano tse amanang le phetolelo ea lipalo ho thusa babali ho utloisisa mohopolo ona hamolemo.
Mehopolo ea Motheo ea Phetolelo
Phetolelo ka dikhokahano tsa mahlakore a mabedi e ka hlahiswa ka ho sebedisa mongolo wa vekthara. Haeba ntlha A(x, y) e fetolelwa ke vekthara \((a, b)\), ntlha e hlahang A' (\(x'\), \(y'\)) e ka balwa ho sebediswa foromo:
\[ x' = x + a \]
\[ y' = y + b \]
Moo:
– \( (x, y) \) ke khokahano ea pele,
– \( (a, b) \) ke vekthara ya phetolelo,
– \( (x', y') \) ke dikhokahano tsa sephetho sa phetolelo.
Lipotso tsa Mehlala le Puisano
Mehlala e meng ea lipotso mabapi le phetolelo ea lipalo le lipuisano tsa tsona ke ena:
Mohlala oa Potso ea 1:
Potso:
Ntlha ea A e ho likhokahano (3, 4). Fetolela ntlha ea A ka vekthara \( (5, -2) \). Fumana likhokahano tse ncha tsa ntlha ea A.
Puisano:
Hoa tsebahala:
\[ \text{Likhokahano tsa mantlha tsa ntlha A} = (3, 4) \]
\[ \text{Phetolelo vekthara} = (5, -2) \]
Sebelisa foromo ea phetolelo:
\[ x' = x + a \]
\[ y' = y + b \]
Kenya boleng sebakeng sa bona:
\[x' = 3 + 5 = 8 \]
\[ y' = 4 + (-2) = 2 \]
Kahoo, likhokahano tse ncha tsa ntlha ea A kamora phetolelo ke \( (8, 2) \).
Mohlala oa Potso ea 2:
Potso:
Khutlotharo e na le dikhokahano tsa vertex \( A(1, 2) \), \( B(3, 5) \), le \( C(6, 1) \). Fetolela khutlotharo ka vekthara \( (-2, 4) \). Fumana dikhokahano tsa vertex tsa khutlotharo kamora phetolelo.
Puisano:
Likhokahano tsa ntlha ea khutlotharo le vekthara ea phetolelo lia tsebahala.
Likhokahano tsa ntlha A':
\[ x' = 1 + (-2) = -1 \]
\[ y' = 2 + 4 = 6 \]
Ebe, \( A' = (-1, 6) \).
Likhokahano tsa ntlha ea B':
\[ x' = 3 + (-2) = 1 \]
\[ y' = 5 + 4 = 9 \]
Ebe, \( B' = (1, 9) \).
Likhokahano tsa ntlha C':
\[ x' = 6 + (-2) = 4 \]
\[ y' = 1 + 4 = 5 \]
Ebe, \( C' = (4, 5) \).
Kahoo, kamora phetolelo, dikhokahano tsa di-vertise tsa khutlotharo e ntjha ke \( A'(-1, 6) \), \( B'(1, 9) \), le \( C'(4, 5) \).
Mohlala oa Potso ea 3:
Potso:
Ntlha e fanoeng P ho li-coordinates \( (-3, 0) \). Fumana sephetho sa phetolelo ea ntlha P ka vector \( (7, -5) \).
Puisano:
Ho fanoe ka likhokahano tsa P le vekthara ea phetolelo.
Sebelisa foromo ea phetolelo:
\[ x' = x + a \]
\[ y' = y + b \]
Kenya boleng sebakeng sa bona:
\[ x' = -3 + 7 = 4 \]
\[ y' = 0 + (-5) = -5 \]
Kahoo, likhokahano tsa sephetho sa phetolelo sa ntlha P ke \( (4, -5) \).
Mohlala oa Potso ea 4:
Potso:
Ntlha ea Q e fumaneha ho likhokahano \((4, -3) \). Haeba ntlha ea Q e fetoleloa e le hore likhokahano tse ncha li fetohe \((9, 1) \), fumana vekthara ea phetolelo e sebelisitsoeng.
Puisano:
Hoa tsebahala:
\[ \text{Li-coordinates tsa pele} = (4, -3) \]
\[ \text{Dikoordinatere tsa sephetho} = (9, 1) \]
Sebelisa foromo ea phetolelo ho fumana vekthara \( (a, b) \):
\[ x' = x + a \]
\[ y' = y + b \]
Liphetho tsa phetolelo lia tsebahala:
\[9 = 4 + a \]
\[ 1 = -3 + b \]
Kahoo, vekthara ea phetolelo e ka baloa ka tsela e latelang:
\[a = 9 – 4 = 5 \]
\[b = 1 + 3 = 4 \]
Kahoo, vekthara ea phetolelo e sebelisitsoeng ke \( (5, 4) \).
Mohlala oa Potso ea 5:
Potso:
ABCD e nang le mahlakore a mane e na le dintlha tsa sekhutlo \( A(1, 2) \), \( B(1, 5) \), \( C(4, 5) \), le \( D(4, 2) \). Fetolela mahlakore a mane ka vekthara \( (3, -1) \). Fumana dikhokahano tse ntjha tsa mahlakore a mane a mane a ABCD.
Puisano:
Hoa tsebahala:
\[ \text{Phetolelo vekthara} = (3, -1) \]
Likhokahano tsa ntlha A':
\[x' = 1 + 3 = 4 \]
\[ y' = 2 + (-1) = 1 \]
Ebe, \( A' = (4, 1) \).
Likhokahano tsa ntlha ea B':
\[x' = 1 + 3 = 4 \]
\[ y' = 5 + (-1) = 4 \]
Ebe, \( B' = (4, 4) \).
Likhokahano tsa ntlha C':
\[x' = 4 + 3 = 7 \]
\[ y' = 5 + (-1) = 4 \]
Ebe, \( C' = (7, 4) \).
Likhokahano tsa ntlha D':
\[x' = 4 + 3 = 7 \]
\[ y' = 2 + (-1) = 1 \]
Ebe, \( D' = (7, 1) \).
Kahoo, likhokahano tse ncha tsa quadrilateral ABCD kamora phetolelo ke \( A'(4, 1) \), \( B'(4, 4) \), \( C'(7, 4) \), le \( D'(7, 1) \).
Qetello
Phetolelo ke phetoho ea motheo haholo empa e le ea bohlokoa ho jiometri. Ho tseba mokhoa ona ho re lumella ho etsa mesebetsi e fapaneng ea jiometri, joalo ka ho suthisa lintho ntle le ho fetola sebopeho kapa boholo ba tsona.
Ka ho utloisisa mohopolo oa phetolelo ka mehlala e fapaneng ea mathata a tšohliloeng ka holimo, ho tšeptjoa hore babali ba tla khona ho utloisisa le ho sebelisa mohopolo ona hamolemo mathateng a fapaneng le bophelong ba sebele. Phetolelo ha e na thuso feela lipalo empa hape le mafapheng a mang a fapaneng, ho kenyeletsoa fisiks, litšoantšo tsa khomphutha le moralo.
