Roboguru

Translasi  memetakan titik  ke titik . a. Tentukan translasi tersebut! b. Tentukanlah bayangan segitiga  dengan titik sudut , , dan  oleh translasi tersebut! c. Jika segitiga yang diperoleh pada jawaban b ditranslasikan lagi dengan , tentukan bayangannya! d. Translasikan segitiga  dengan translasi  dan . Samakah jawabannya dengan jawaban c?

Pertanyaan

Translasi begin mathsize 14px style text T end text subscript 1 equals open parentheses table row p row q end table close parentheses end style memetakan titik begin mathsize 14px style text A end text open parentheses 1 comma space 2 close parentheses end style ke titik begin mathsize 14px style text A' end text open parentheses 4 comma space 6 close parentheses end style.

a. Tentukan translasi tersebut!

b. Tentukanlah bayangan segitiga begin mathsize 14px style text ABC end text end style dengan titik sudut undefinedbegin mathsize 14px style text B end text open parentheses 3 comma space 4 close parentheses end style, dan begin mathsize 14px style text C end text open parentheses 5 comma space 6 close parentheses end style oleh translasi tersebut!

c. Jika segitiga yang diperoleh pada jawaban b ditranslasikan lagi dengan begin mathsize 14px style text T end text subscript 2 equals open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end style, tentukan bayangannya!

d. Translasikan segitiga begin mathsize 14px style text ABC end text end style dengan translasi begin mathsize 14px style text T end text subscript 2 equals open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end style dan begin mathsize 14px style text T end text subscript 1 equals open parentheses table row p row q end table close parentheses end style. Samakah jawabannya dengan jawaban c?

  1. ...undefined 

  2. ...undefined 

Pembahasan Soal:

Perhatikan penjabaran berikut ini.

a.  begin mathsize 14px style text A end text open parentheses 1 comma space 2 close parentheses end style ke titik begin mathsize 14px style text A' end text open parentheses 4 comma space 6 close parentheses end style ditranslasikan oleh:

begin mathsize 14px style text T end text subscript 1 equals open parentheses table row cell x apostrophe minus x end cell row cell y apostrophe minus y end cell end table close parentheses equals open parentheses table row cell 4 minus 1 end cell row cell 6 minus 2 end cell end table close parentheses equals open parentheses table row 3 row 4 end table close parentheses end style

b.  Bayangan segitiga begin mathsize 14px style text ABC end text end style dengan titik sudut undefinedbegin mathsize 14px style text B end text open parentheses 3 comma space 4 close parentheses end style, dan begin mathsize 14px style text C end text open parentheses 5 comma space 6 close parentheses end style ditrsnlasikan oleh translasi begin mathsize 14px style text T end text subscript 1 end style, yaitu:

begin mathsize 14px style text A end text open parentheses x comma space y close parentheses rightwards arrow with text T end text subscript 1 equals open parentheses p comma space q close parentheses on top text A' end text open parentheses x apostrophe comma space y apostrophe close parentheses equals open parentheses x plus p comma space y plus q close parentheses text A end text open parentheses 1 comma space 2 close parentheses rightwards arrow with text T end text subscript 1 equals open parentheses 3 comma space 4 close parentheses on top text A' end text open parentheses x apostrophe comma space y apostrophe close parentheses equals open parentheses 1 plus 3 comma space 2 plus 4 close parentheses equals open parentheses 4 comma space 6 close parentheses text B end text open parentheses 3 comma space 4 close parentheses rightwards arrow with text T end text subscript 1 equals open parentheses 3 comma space 4 close parentheses on top text B' end text open parentheses x apostrophe comma space y apostrophe close parentheses equals open parentheses 3 plus 3 comma space 4 plus 4 close parentheses equals open parentheses 6 comma space 8 close parentheses text C end text open parentheses 5 comma space 6 close parentheses rightwards arrow with text T end text subscript 1 equals open parentheses 3 comma space 4 close parentheses on top text C' end text open parentheses x apostrophe comma space y apostrophe close parentheses equals open parentheses 5 plus 3 comma space 6 plus 4 close parentheses equals open parentheses 8 comma space 10 close parentheses end style

c. Segitiga yang diperoleh pada jawaban b ditranslasikan lagi dengan begin mathsize 14px style text T end text subscript 2 equals open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end style, maka bayangannya:

begin mathsize 12px style text A' end text left parenthesis x comma space y right parenthesis rightwards arrow with text T end text subscript 2 equals left parenthesis a comma space b right parenthesis on top text A'' end text left parenthesis x apostrophe apostrophe comma space y apostrophe apostrophe right parenthesis equals left parenthesis x plus a comma space y plus b right parenthesis text A' end text left parenthesis 4 comma space 6 right parenthesis rightwards arrow with text T end text subscript 2 equals left parenthesis negative 1 comma space minus 1 right parenthesis on top text A'' end text left parenthesis x apostrophe apostrophe comma space y apostrophe apostrophe right parenthesis equals left parenthesis 4 plus open parentheses negative 1 close parentheses comma space 6 plus open parentheses negative 1 close parentheses right parenthesis equals left parenthesis 3 comma space 5 right parenthesis text B' end text left parenthesis 6 comma space 8 right parenthesis rightwards arrow with text T end text subscript 2 equals left parenthesis negative 1 comma space minus 1 right parenthesis on top text B'' end text left parenthesis x apostrophe apostrophe comma space y apostrophe apostrophe right parenthesis equals left parenthesis 6 plus open parentheses negative 1 close parentheses comma space 8 plus open parentheses negative 1 close parentheses right parenthesis equals left parenthesis 5 comma space 7 right parenthesis text C' end text left parenthesis 8 comma space 10 right parenthesis rightwards arrow with text T end text subscript 2 equals left parenthesis negative 1 comma space minus 1 right parenthesis on top text C'' end text left parenthesis x apostrophe apostrophe comma space y apostrophe apostrophe right parenthesis equals left parenthesis 8 plus open parentheses negative 1 close parentheses comma space 10 plus open parentheses negative 1 close parentheses right parenthesis equals left parenthesis 7 comma space 9 right parenthesis end style

d. Translasikan segitiga begin mathsize 14px style text ABC end text end style dengan translasi begin mathsize 14px style text T end text subscript 2 equals open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end style dan begin mathsize 14px style text T end text subscript 1 equals open parentheses table row p row q end table close parentheses end style, samakah dengan hasil c?

begin mathsize 14px style text A end text left parenthesis x comma space y right parenthesis rightwards arrow with text T end text subscript 2 equals left parenthesis a comma space b right parenthesis on top text A' end text left parenthesis x apostrophe comma space y apostrophe right parenthesis equals left parenthesis x plus a comma space y plus b right parenthesis text A end text left parenthesis 1 comma space 2 right parenthesis rightwards arrow with text T end text subscript 2 equals left parenthesis negative 1 comma space minus 1 right parenthesis on top text A' end text left parenthesis x apostrophe comma space y apostrophe right parenthesis equals left parenthesis 1 plus open parentheses negative 1 close parentheses comma space 2 plus open parentheses negative 1 close parentheses right parenthesis equals left parenthesis 0 comma space 1 right parenthesis text B end text left parenthesis 3 comma space 4 right parenthesis rightwards arrow with text T end text subscript 2 equals left parenthesis negative 1 comma space minus 1 right parenthesis on top text B' end text left parenthesis x apostrophe comma space y apostrophe right parenthesis equals left parenthesis 3 plus left parenthesis negative 1 right parenthesis comma space 4 plus left parenthesis negative 1 right parenthesis right parenthesis equals left parenthesis 2 comma space 3 right parenthesis text C end text left parenthesis 5 comma space 6 right parenthesis rightwards arrow with text T end text subscript 2 equals left parenthesis negative 1 comma space minus 1 right parenthesis on top text C' end text left parenthesis x apostrophe comma space y apostrophe right parenthesis equals left parenthesis 5 plus left parenthesis negative 1 right parenthesis comma space 6 plus left parenthesis negative 1 right parenthesis right parenthesis equals left parenthesis 4 comma space 5 right parenthesis end style

kemudian

begin mathsize 14px style text A' end text left parenthesis x comma space y right parenthesis rightwards arrow with text T end text subscript 1 equals left parenthesis p comma space q right parenthesis on top text A'' end text left parenthesis x apostrophe apostrophe comma space y apostrophe apostrophe right parenthesis equals left parenthesis x plus p comma space y plus q right parenthesis text A' end text left parenthesis 0 comma space 1 right parenthesis rightwards arrow with text T end text subscript 1 equals left parenthesis 3 comma space 4 right parenthesis on top text A'' end text left parenthesis x apostrophe apostrophe comma space y apostrophe apostrophe right parenthesis equals left parenthesis 0 plus 3 comma space 1 plus 4 right parenthesis equals left parenthesis 3 comma space 5 right parenthesis text B' end text left parenthesis 2 comma space 3 right parenthesis rightwards arrow with text T end text subscript 1 equals left parenthesis 3 comma space 4 right parenthesis on top text B'' end text left parenthesis x apostrophe apostrophe comma space y apostrophe apostrophe right parenthesis equals left parenthesis 2 plus 3 comma space 3 plus 4 right parenthesis equals left parenthesis 5 comma space 7 right parenthesis text C' end text left parenthesis 4 comma space 5 right parenthesis rightwards arrow with text T end text subscript 1 equals left parenthesis 3 comma space 4 right parenthesis on top text C'' end text left parenthesis x apostrophe apostrophe comma space y apostrophe apostrophe right parenthesis equals left parenthesis 4 plus 3 comma space 5 plus 4 right parenthesis equals left parenthesis 7 comma space 9 right parenthesis end style

Hasil bayangan sama dengan hasil bayangan di jawaban c.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 08 Februari 2021

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