Roboguru

Diketahui segitiga  dengan koordinat titik sudut di , dan  didilatasi dengan menggunakan faktor skala  dengan pusat titik asal kemudian dirotasi  searah jarum jam yang berpusat di titik asal. Bayangan hasil transformasinya adalah ....

Pertanyaan

Diketahui segitiga ABC dengan koordinat titik sudut di straight A open parentheses 6 comma space 12 close parentheses comma space straight B open parentheses negative 9 comma space 3 close parentheses, dan straight C open parentheses 6 comma space minus 6 close parentheses didilatasi dengan menggunakan faktor skala 1 third dengan pusat titik asal kemudian dirotasi 90 degree searah jarum jam yang berpusat di titik asal. Bayangan hasil transformasinya adalah ....

  1. straight A apostrophe open parentheses 2 comma space 4 close parentheses comma space straight B apostrophe open parentheses negative 3 comma space 1 close parentheses comma space straight C apostrophe open parentheses 2 comma space minus 2 close parentheses 

  2. straight A apostrophe open parentheses 2 comma space minus 4 close parentheses comma space straight B apostrophe open parentheses negative 3 comma space 1 close parentheses comma space straight C apostrophe open parentheses 2 comma space minus 2 close parentheses 

  3. straight A apostrophe open parentheses 2 comma space 4 close parentheses comma space straight B apostrophe open parentheses 3 comma space minus 1 close parentheses comma space straight C apostrophe open parentheses 2 comma space minus 2 close parentheses 

  4. straight A apostrophe open parentheses 2 comma space minus 4 close parentheses comma space straight B apostrophe open parentheses negative 3 comma space 1 close parentheses comma space straight C apostrophe open parentheses negative 2 comma space 2 close parentheses 

Pembahasan Soal:

Ingat kembali:

straight A open parentheses straight x comma space straight y close parentheses rightwards arrow with open square brackets open parentheses straight o comma straight o close parentheses comma space straight k close square brackets on top straight A apostrophe open parentheses kx comma space ky close parentheses straight A open parentheses straight x comma space straight y close parentheses rightwards arrow with straight R open parentheses 90 degree close parentheses on top straight A apostrophe open parentheses straight y comma space minus straight x close parentheses    

Diketahui:

straight A open parentheses 6 comma space 12 close parentheses comma space straight B open parentheses negative 9 comma space 3 close parentheses comma space straight C open parentheses 6 comma space minus 6 close parentheses 

Maka:

 straight A open parentheses 6 comma space 12 close parentheses rightwards arrow with open square brackets open parentheses 0 comma 0 close parentheses comma space 1 third close square brackets on top open parentheses 2 comma space 4 close parentheses rightwards arrow with straight R open parentheses 90 degree close parentheses on top straight A apostrophe open parentheses 4 comma space minus 2 close parentheses straight B open parentheses negative 9 comma space 3 close parentheses rightwards arrow with open square brackets open parentheses 0 comma 0 close parentheses comma space 1 third close square brackets on top open parentheses negative 3 comma space 1 close parentheses rightwards arrow with straight R open parentheses 90 degree close parentheses on top straight B apostrophe open parentheses 1 comma space 3 close parentheses straight C open parentheses 6 comma space minus 6 close parentheses rightwards arrow with open square brackets open parentheses 0 comma 0 close parentheses comma space 1 third close square brackets on top open parentheses 2 comma space minus 2 close parentheses rightwards arrow with straight R open parentheses 90 degree close parentheses on top straight A apostrophe open parentheses negative 2 comma space minus 2 close parentheses

Jadi, jawaban yang benar adalah straight A apostrophe open parentheses 4 comma space minus 2 close parentheses comma space straight B apostrophe open parentheses 1 comma space 3 close parentheses comma space straight C apostrophe open parentheses negative 2 comma space minus 2 close parentheses sehingga tidak ada pilihan ajwaban yang sesuai.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

W. Lestari

Mahasiswa/Alumni Universitas Sriwijaya

Terakhir diupdate 30 April 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui segi empat  dengan koordinat titik sudut di , dan . Gambar bayangan hasil transformasinya jika diketahui segi empat tersebut: a. Ditranslasi  satuan ke kanan dan  satuan ke bawah kemudian d...

Pembahasan Soal:

a. Ditranslasi 3 satuan ke kanan dan 5 satuan ke bawah

    Error converting from MathML to accessible text.     

    kemudian dicerminkan terhadap sumbu-x begin mathsize 14px style colon left parenthesis straight x comma straight y right parenthesis rightwards arrow left parenthesis straight x comma negative straight y right parenthesis end style menjadi

    begin mathsize 14px style straight A apostrophe left parenthesis 5 comma 0 right parenthesis rightwards arrow straight A apostrophe apostrophe left parenthesis 5 comma 0 right parenthesis straight B apostrophe left parenthesis 0 comma negative 1 right parenthesis rightwards arrow straight B apostrophe apostrophe left parenthesis 0 comma 1 right parenthesis straight C apostrophe left parenthesis 7 comma negative 2 right parenthesis rightwards arrow straight C apostrophe apostrophe left parenthesis 7 comma 2 right parenthesis straight D apostrophe left parenthesis 7 comma negative 7 right parenthesis rightwards arrow straight D apostrophe apostrophe left parenthesis 7 comma 7 right parenthesis end style  

    

b. Dirotasi begin mathsize 14px style 90 degree end style dengan pusat titik asal Error converting from MathML to accessible text. menjadi 

    undefined    

    kemudian ditranslasi begin mathsize 14px style left parenthesis straight x minus 3 comma straight y plus 2 right parenthesis end style menjadi

    straight A apostrophe apostrophe left parenthesis negative 5 minus 3 comma 2 plus 2 right parenthesis equals straight A double apostrophe left parenthesis negative 8 comma 4 right parenthesis straight B apostrophe apostrophe left parenthesis negative 4 minus 3 comma negative 3 plus 2 right parenthesis equals straight B double apostrophe left parenthesis negative 7 comma negative 1 right parenthesis straight C apostrophe apostrophe left parenthesis negative 3 minus 3 comma 4 plus 2 right parenthesis equals straight C double apostrophe left parenthesis negative 6 comma 6 right parenthesis straight D apostrophe apostrophe left parenthesis 2 minus 3 comma 4 plus 2 right parenthesis equals straight D apostrophe apostrophe left parenthesis negative 1 comma 6 right parenthesis    

      

c. Ditranslasi open parentheses table row 3 row 6 end table close parentheses menjadi

    Error converting from MathML to accessible text.        

    dilatasi dengan faktor skala 2

    begin mathsize 14px style straight A apostrophe left parenthesis 5 comma 11 right parenthesis rightwards arrow straight A double apostrophe left parenthesis 10 comma 22 right parenthesis straight B apostrophe left parenthesis 0 comma 10 right parenthesis rightwards arrow straight B double apostrophe left parenthesis 0 comma 20 right parenthesis straight C apostrophe left parenthesis 7 comma 9 right parenthesis rightwards arrow straight C double apostrophe left parenthesis 14 comma 18 right parenthesis straight D apostrophe left parenthesis 7 comma 4 right parenthesis rightwards arrow straight D double apostrophe left parenthesis 14 comma 8 right parenthesis end style 

     

Roboguru

Bangun berwarna biru merupakan bayangan hasil transformasi dari bangun berwarna merah. Sebutkan langkah-langkah tranformasi yang dilakukan terhadap bangun berwarna merah sehingga diperoleh bayangan be...

Pembahasan Soal:

a. Ditranslasi 5 satuan ke atas menjadi

    size 14px left parenthesis size 14px 4 size 14px comma size 14px minus size 14px 2 size 14px plus size 14px 5 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px 4 size 14px comma size 14px 3 size 14px right parenthesis size 14px left parenthesis size 14px 1 size 14px comma size 14px minus size 14px 2 size 14px plus size 14px 5 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px 1 size 14px comma size 14px 3 size 14px right parenthesis size 14px left parenthesis size 14px 1 size 14px comma size 14px minus size 14px 4 size 14px plus size 14px 5 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px 1 size 14px comma size 14px 1 size 14px right parenthesis size 14px left parenthesis size 14px 4 size 14px comma size 14px minus size 14px 4 size 14px plus size 14px 5 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px 4 size 14px comma size 14px 1 size 14px right parenthesis     

    Dirotasikan begin mathsize 14px style 90 degree end style berlawanan arah jarum jam Error converting from MathML to accessible text. menjadi

    size 14px left parenthesis size 14px 4 size 14px comma size 14px 3 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px minus size 14px 3 size 14px comma size 14px 4 size 14px right parenthesis size 14px left parenthesis size 14px 1 size 14px comma size 14px 3 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px minus size 14px 3 size 14px comma size 14px 1 size 14px right parenthesis size 14px left parenthesis size 14px 1 size 14px comma size 14px 1 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px minus size 14px 1 size 14px comma size 14px 1 size 14px right parenthesis size 14px left parenthesis size 14px 4 size 14px comma size 14px 1 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px minus size 14px 1 size 14px comma size 14px 4 size 14px right parenthesis  

b. Ditranslasi ke kiri 1 satuan dan ke atas 1 satuan menjadi

    size 14px left parenthesis size 14px 1 size 14px minus size 14px 1 size 14px comma size 14px 2 size 14px plus size 14px 1 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px 0 size 14px comma size 14px 3 size 14px right parenthesis size 14px left parenthesis size 14px 1 size 14px minus size 14px 1 size 14px comma size 14px 0 size 14px plus size 14px 1 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px 0 size 14px comma size 14px 1 size 14px right parenthesis size 14px left parenthesis size 14px 5 size 14px minus size 14px 1 size 14px comma size 14px 2 size 14px plus size 14px 1 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px 4 size 14px comma size 14px 3 size 14px right parenthesis 

    Dirotasikan begin mathsize 14px style 90 degree end style berlawanan arah jarum jam undefined menjadi 

    size 14px left parenthesis size 14px 0 size 14px comma size 14px 3 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px minus size 14px 3 size 14px comma size 14px 0 size 14px right parenthesis size 14px left parenthesis size 14px 0 size 14px comma size 14px 1 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px minus size 14px 1 size 14px comma size 14px 0 size 14px right parenthesis size 14px left parenthesis size 14px 4 size 14px comma size 14px 3 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px minus size 14px 3 size 14px comma size 14px 4 size 14px right parenthesis    

c. Didilatasi 3 menjadi 

    size 14px left parenthesis size 14px 2 size 14px comma size 14px minus size 14px 4 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px 6 size 14px comma size 14px minus size 14px 12 size 14px right parenthesis size 14px left parenthesis size 14px 2 size 14px comma size 14px minus size 14px 2 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px 6 size 14px comma size 14px minus size 14px 6 size 14px right parenthesis size 14px left parenthesis size 14px 5 size 14px comma size 14px minus size 14px 4 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px 15 size 14px comma size 14px minus size 14px 12 size 14px right parenthesis 

    Ditranslasi 11 satuan ke kiri dan 11 satuan ke atas menjadi

    size 14px left parenthesis size 14px 6 size 14px minus size 14px 11 size 14px comma size 14px minus size 14px 12 size 14px plus size 14px 11 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px minus size 14px 5 size 14px comma size 14px minus size 14px 1 size 14px right parenthesis size 14px left parenthesis size 14px 6 size 14px minus size 14px 11 size 14px comma size 14px minus size 14px 6 size 14px plus size 14px 11 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px minus size 14px 5 size 14px comma size 14px 5 size 14px right parenthesis size 14px left parenthesis size 14px 15 size 14px minus size 14px 11 size 14px comma size 14px minus size 14px 12 size 14px plus size 14px 11 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px 4 size 14px comma size 14px minus size 14px 1 size 14px right parenthesis 

d. Didilatasi 2 menjadi

   size 14px left parenthesis size 14px 4 size 14px comma size 14px 3 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px 8 size 14px comma size 14px 6 size 14px right parenthesis size 14px left parenthesis size 14px 2 size 14px comma size 14px 3 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px 4 size 14px comma size 14px 6 size 14px right parenthesis size 14px left parenthesis size 14px 3 size 14px comma size 14px 1 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px 6 size 14px comma size 14px 2 size 14px right parenthesis size 14px left parenthesis size 14px 1 size 14px comma size 14px 1 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px 2 size 14px comma size 14px 2 size 14px right parenthesis 

   Dirotasikan begin mathsize 14px style 90 degree end style berlawanan arah jarum jam undefined menjadi

   size 14px left parenthesis size 14px 8 size 14px comma size 14px 6 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px minus size 14px 6 size 14px comma size 14px 8 size 14px right parenthesis size 14px left parenthesis size 14px 4 size 14px comma size 14px 6 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px minus size 14px 6 size 14px comma size 14px 4 size 14px right parenthesis size 14px left parenthesis size 14px 6 size 14px comma size 14px 2 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px minus size 14px 2 size 14px comma size 14px 6 size 14px right parenthesis size 14px left parenthesis size 14px 2 size 14px comma size 14px 2 size 14px right parenthesis size 14px rightwards arrow size 14px left parenthesis size 14px minus size 14px 2 size 14px comma size 14px 2 size 14px right parenthesis 

e. Ditranslasi ke kiri 5 satuan dan ke atas 5 satuan

    size 14px left parenthesis size 14px 2 size 14px minus size 14px 5 size 14px comma size 14px minus size 14px 4 size 14px plus size 14px 5 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px minus size 14px 3 size 14px comma size 14px 1 size 14px right parenthesis size 14px left parenthesis size 14px 2 size 14px minus size 14px 5 size 14px comma size 14px minus size 14px 2 size 14px plus size 14px 5 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px minus size 14px 3 size 14px comma size 14px 3 size 14px right parenthesis size 14px left parenthesis size 14px 4 size 14px minus size 14px 5 size 14px comma size 14px minus size 14px 4 size 14px plus size 14px 5 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px minus size 14px 1 size 14px comma size 14px 1 size 14px right parenthesis size 14px left parenthesis size 14px 4 size 14px minus size 14px 5 size 14px comma size 14px minus size 14px 2 size 14px plus size 14px 5 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px minus size 14px 1 size 14px comma size 14px 3 size 14px right parenthesis  

f. Dirotasikan begin mathsize 14px style 90 degree end style searah jarum jam begin mathsize 14px style left parenthesis straight x comma straight y right parenthesis rightwards arrow left parenthesis straight y comma negative straight x right parenthesis end style menjadi 

   begin mathsize 14px style left parenthesis negative 4 comma 1 right parenthesis rightwards arrow left parenthesis 1 comma 4 right parenthesis left parenthesis negative 1 comma 1 right parenthesis rightwards arrow left parenthesis 1 comma 1 right parenthesis left parenthesis negative 4 comma 4 right parenthesis rightwards arrow left parenthesis 4 comma 4 right parenthesis end style 

   kemudian ditranslasi ke kiri 1 satuan dan ke bawah 1 satuan

   begin mathsize 14px style left parenthesis 1 minus 1 comma 4 minus 1 right parenthesis equals left parenthesis 0 comma 3 right parenthesis left parenthesis 1 minus 1 comma 1 minus 1 right parenthesis equals left parenthesis 0 comma 0 right parenthesis left parenthesis 4 minus 1 comma 4 minus 1 right parenthesis equals left parenthesis 3 comma 3 right parenthesis end style 

Roboguru

Perhatikan tabel di bawah ini! Nomor baris yang benar dari keterangan pada tabel adalah...

Pembahasan Soal:

Ingat :

  1. Refleksi terhadap sumbu x : left parenthesis x apostrophe comma space y apostrophe right parenthesis rightwards arrow left parenthesis x comma negative y right parenthesis 
  2. Rotasi sejauh 90o dan pusat open parentheses 0 comma 0 close parentheses : open parentheses x apostrophe comma space y apostrophe close parentheses rightwards arrow open parentheses negative y comma space x close parentheses
  3. Translasi oleh open parentheses table row a row b end table close parentheses : open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses equals open parentheses table row cell x plus a end cell row cell y plus b end cell end table close parentheses
  4. Dilatasi skala k dan pusat open parentheses 0 comma 0 close parentheses : open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses equals open parentheses table row cell k x end cell row cell k y end cell end table close parentheses

Untuk titik open parentheses 2 comma 3 close parentheses, maka :

  1. Refleksi terhadap sumbu x : left parenthesis x apostrophe comma space y apostrophe right parenthesis rightwards arrow left parenthesis 2 comma negative 3 right parenthesis 
  2. Rotasi sejauh 90o dan pusat open parentheses 0 comma 0 close parentheses : open parentheses x apostrophe comma space y apostrophe close parentheses rightwards arrow open parentheses negative 3 comma space 2 close parentheses
  3. Translasi oleh open parentheses table row 1 row 3 end table close parentheses : open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses equals open parentheses table row cell 2 plus 1 end cell row cell 3 plus 3 end cell end table close parentheses equals open parentheses table row 3 row 6 end table close parentheses
  4. Dilatasi skala 3 dan pusat open parentheses 0 comma 0 close parentheses : open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses equals open parentheses table row cell 3 open parentheses 2 close parentheses end cell row cell 3 open parentheses 3 close parentheses end cell end table close parentheses equals open parentheses table row 6 row 9 end table close parentheses

Jadi, tidak ada jawaban yang tepat pada pilihan jawaban.

Roboguru

Diketahui segitiga   dengan koordinat titik sudut di  dan . Gambar bayangan hasil transformasinya jika diketahui segitiga tersebut: b. Dirotasi  berlawanan arah jarum jam yang berpusat di titik asal ...

Pembahasan Soal:

Rotasi adalah transformasi yang memindahkan titik-titik dengan cara memutar titik-titik tersebut sejauh theta terhadap suatu titik pusat.

Diketahui segitiga  dengan koordinat titik sudut di straight R left parenthesis 3 comma space 6 right parenthesis comma space straight S left parenthesis negative 5 comma space 2 right parenthesis dan

Rotasi 90 degree berlawanan arah jarum jam dengan titik asal , dinotasikan:

straight A open parentheses x comma space y close parentheses rightwards arrow straight A apostrophe open parentheses negative y comma space x close parentheses  

Sehingga diperoleh koordinat bayangan dari segitiga :

  • straight R left parenthesis 3 comma space 6 right parenthesis rightwards arrow straight R apostrophe open parentheses negative 6 comma space 3 close parentheses  
  • straight S left parenthesis negative 5 comma space 2 right parenthesis rightwards arrow straight S apostrophe open parentheses negative 2 comma space minus 5 close parentheses 
  • straight T left parenthesis 3 comma space minus 3 right parenthesis rightwards arrow straight T apostrophe open parentheses 3 comma space 3 close parentheses  

Secara umum dilatasi dari suatu koordinat open parentheses x comma space y close parentheses dengan faktor skala k menghasilkan koordinat open parentheses k x comma space k y close parentheses. Atau dapat dinotasikan: open parentheses x comma space y close parentheses rightwards arrow open parentheses k x comma space k y close parentheses 

Kemudian segitiga  didilatasi dengan faktor skala  berpusat di titik asal, sehingga open parentheses x comma space y close parentheses rightwards arrow open parentheses 2 x comma space 2 y close parentheses

  • straight R apostrophe open parentheses negative 6 comma space 3 close parentheses rightwards arrow straight R apostrophe apostrophe open parentheses negative 12 comma space 6 close parentheses    
  • straight S apostrophe open parentheses negative 2 comma space minus 5 close parentheses rightwards arrow straight S apostrophe apostrophe open parentheses negative 4 comma space minus 10 close parentheses  
  • straight T apostrophe open parentheses 3 comma space 3 close parentheses rightwards arrow straight T apostrophe apostrophe open parentheses 6 comma space 6 close parentheses    

Jadi, gambar bayangan hasil transformasi segitiga  adalah sebagai berikut.


Roboguru

Tentukan persamaan bayangan dari titik  oleh rotasi sebesar  searah jarum jam dilanjutkan dilatasi dengan faktor skala .

Pembahasan Soal:

Mencari bayangan hasil rotasi:

space space space space space straight B left parenthesis x comma space y right parenthesis rightwards arrow with straight R space 90 degree on top straight B apostrophe left parenthesis y comma space minus x right parenthesis straight B left parenthesis 12 comma space minus 8 right parenthesis rightwards arrow with straight R space 90 degree on top straight B apostrophe left parenthesis negative 8 comma space minus 12 right parenthesis 

Mencari bayangan hasil dilatasi:

space space space space space space space space space straight B apostrophe left parenthesis x comma space y right parenthesis rightwards arrow with k equals negative 1 half on top straight B apostrophe apostrophe left parenthesis k x comma space k y right parenthesis straight B apostrophe left parenthesis negative 8 comma space minus 12 right parenthesis rightwards arrow with k equals negative 1 half on top straight B apostrophe apostrophe open parentheses open parentheses negative 1 half close parentheses minus 8 comma space open parentheses negative 1 half close parentheses minus 12 close parentheses straight B apostrophe left parenthesis negative 8 comma space minus 12 right parenthesis rightwards arrow with k equals negative 1 half on top straight B apostrophe apostrophe open parentheses 4 comma space 6 close parentheses 

Jadi, bayangannya adalah straight B apostrophe apostrophe left parenthesis 4 comma space 6 right parenthesis.

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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