Pertanyaan

Diketahui titik-titik P ( 2 , 1 ) , Q ( 4 , 1 ) , R ( 4 , 3 ) , dan S ( 2 , 3 ) didilatasi terhadap pusat O ( 0 , 0 ) dan faktor skala = 3 . Tentukan: b. bayangan garis PQ , PR , dan QS , dan ( Kinomatika 2013 )

Diketahui titik-titik $P (2, 1)$ , $Q (4, 1)$ , $R (4, 3)$ , dan $S (2, 3)$ didilatasi terhadap pusat $O (0, 0)$ dan $faktor skala = 3$ . Tentukan:

b. bayangan garis $PQ$ , $PR$ , dan $QS$ , dan

(Kinomatika 2013)

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Jawaban terverifikasi

Pembahasan

Diketahui pada bagian a bahwa bayangan titik-titik tersebut adalah Maka, bayangan garisnya adalah garis : garis : garis : Jadi, bayangan garis berturut-turut adalah .

Diketahui pada bagian a bahwa bayangan titik-titik tersebut adalah P apostrophe left parenthesis 6 comma space 3 right parenthesis comma space Q apostrophe left parenthesis 12 comma space 3 right parenthesis comma space R apostrophe left parenthesis 12 comma space 9 right parenthesis comma space S apostrophe left parenthesis 6 comma space 9 right parenthesis

Maka, bayangan garisnya adalah

garis :

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator y minus y subscript P apostrophe end subscript over denominator y subscript Q apostrophe end subscript minus y subscript P apostrophe end subscript end fraction end cell equals cell fraction numerator x minus x subscript P apostrophe end subscript over denominator x subscript Q apostrophe end subscript minus x subscript P apostrophe end subscript end fraction end cell row cell fraction numerator y minus 3 over denominator 3 minus 3 end fraction end cell equals cell fraction numerator x minus 6 over denominator 12 minus 6 end fraction end cell row cell fraction numerator y minus 3 over denominator 0 end fraction end cell equals cell fraction numerator x minus 6 over denominator 6 end fraction end cell row cell 6 left parenthesis y minus 3 right parenthesis end cell equals cell 0 left parenthesis x minus 6 right parenthesis end cell row cell 6 y minus 18 end cell equals 0 row cell 6 y end cell equals 18 row y equals 3 end table$

garis :

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator y minus y subscript P apostrophe end subscript over denominator y subscript R apostrophe end subscript minus y subscript P apostrophe end subscript end fraction end cell equals cell fraction numerator x minus x subscript P apostrophe end subscript over denominator x subscript R apostrophe end subscript minus x subscript P apostrophe end subscript end fraction end cell row cell fraction numerator y minus 3 over denominator 9 minus 3 end fraction end cell equals cell fraction numerator x minus 6 over denominator 12 minus 6 end fraction end cell row cell fraction numerator y minus 3 over denominator 6 end fraction end cell equals cell fraction numerator x minus 6 over denominator 6 end fraction end cell row cell 6 left parenthesis y minus 3 right parenthesis end cell equals cell 6 left parenthesis x minus 6 right parenthesis end cell row cell y minus 3 end cell equals cell x minus 6 end cell row y equals cell x minus 6 plus 3 end cell row y equals cell x minus 3 end cell end table$

garis :

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator y minus y subscript Q apostrophe end subscript over denominator y subscript S apostrophe end subscript minus y subscript Q apostrophe end subscript end fraction end cell equals cell fraction numerator x minus x subscript Q apostrophe end subscript over denominator x subscript S apostrophe end subscript minus x subscript Q apostrophe end subscript end fraction end cell row cell fraction numerator y minus 3 over denominator 9 minus 3 end fraction end cell equals cell fraction numerator x minus 12 over denominator 6 minus 12 end fraction end cell row cell fraction numerator y minus 3 over denominator 6 end fraction end cell equals cell fraction numerator x minus 12 over denominator negative 6 end fraction end cell row cell negative 6 left parenthesis y minus 3 right parenthesis end cell equals cell 6 left parenthesis x minus 12 right parenthesis end cell row cell negative y plus 3 end cell equals cell x minus 12 end cell row cell negative y end cell equals cell x minus 12 minus 3 end cell row cell negative y end cell equals cell x minus 15 end cell row y equals cell 15 minus x end cell end table$

Jadi, bayangan garis P Q comma space P R comma space dan space Q S berturut-turut adalah y equals 3 comma space space y equals x minus 3 comma space y equals 15 minus x .