Roboguru

Segitiga ABC dengan koordinat titik A(-1,2), B(6,-1), dan C(5,2). Segitiga tersebut dirotasi sejauh 180∘ dengan pusat (2, -1). Koordinat bayangan segitiga ABC adalah....

Pertanyaan

Segitiga ABC dengan koordinat titik A(-1,2), B(6,-1), dan C(5,2). Segitiga tersebut dirotasi sejauh 180 degree dengan pusat (2, -1). Koordinat bayangan segitiga ABC adalah....

  1. A'(-4,5), B'(-2,0), C'(-1,-4)

  2. A'(5,-4), B'(2,0), C'(-1,-4)

  3. A'(5,-4), B'(-2,0), C'(-1,-4)

  4. A'(5,4), B'(0,-2), C'(-4,-1)

  5. A'(5,4), B'(2,0),C'(4,-1)

Pembahasan:

R o t a s i space d e n g a n space p u s a t space left parenthesis a comma b right parenthesis space d a n space s u d u t space theta space a d a l a h  open parentheses table row cell x to the power of apostrophe minus a end cell row cell y to the power of apostrophe minus b end cell end table close parentheses equals open parentheses table row cell cos invisible function application theta end cell cell negative sin invisible function application theta end cell row cell sin invisible function application theta end cell cell cos invisible function application theta end cell end table close parentheses open parentheses table row cell x minus a end cell row cell y minus b end cell end table close parentheses  R o t a s i space d e n g a n space p u s a t space left parenthesis 2 comma negative 1 right parenthesis space d a n space s u d u t space 180 to the power of o space a d a l a h  open parentheses table row cell x to the power of apostrophe minus 2 end cell row cell y to the power of apostrophe minus open parentheses negative 1 close parentheses end cell end table close parentheses equals open parentheses table row cell cos invisible function application 180 to the power of o end cell cell negative sin invisible function application 180 to the power of o end cell row cell sin invisible function application 180 to the power of o end cell cell cos invisible function application 180 to the power of o end cell end table close parentheses open parentheses table row cell x minus 2 end cell row cell y minus open parentheses negative 1 close parentheses end cell end table close parentheses  open parentheses table row cell x to the power of apostrophe minus 2 end cell row cell y to the power of apostrophe plus 1 end cell end table close parentheses equals open parentheses table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses open parentheses table row cell x minus 2 end cell row cell y plus 1 end cell end table close parentheses  T i t i k space A left parenthesis negative 1 comma 2 right parenthesis  open parentheses table row cell x to the power of apostrophe minus 2 end cell row cell y to the power of apostrophe plus 1 end cell end table close parentheses equals open parentheses table row cell cos invisible function application 180 degree end cell cell negative sin invisible function application 180 degree end cell row cell sin invisible function application 180 degree end cell cell cos invisible function application 180 degree end cell end table close parentheses open parentheses table row cell negative 1 minus 2 end cell row cell 2 plus 1 end cell end table close parentheses  open parentheses table row cell x to the power of apostrophe minus 2 end cell row cell y to the power of apostrophe plus 1 end cell end table close parentheses equals open parentheses table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses open parentheses table row cell negative 3 end cell row 3 end table close parentheses  open parentheses table row cell x to the power of apostrophe minus 2 end cell row cell y to the power of apostrophe plus 1 end cell end table close parentheses equals open parentheses table row 3 row cell negative 3 end cell end table close parentheses  D i d a p a t  x to the power of apostrophe minus 2 equals 3 left right double arrow x to the power of apostrophe equals 5  y to the power of apostrophe plus 1 equals negative 3 left right double arrow y to the power of apostrophe equals negative 4  M a k a A to the power of apostrophe left parenthesis 5 comma negative 4 right parenthesis    T i t i k space B left parenthesis 6 comma negative 2 right parenthesis  open parentheses table row cell x to the power of apostrophe minus 2 end cell row cell y to the power of apostrophe plus 1 end cell end table close parentheses equals open parentheses table row cell cos invisible function application 180 degree end cell cell negative sin invisible function application 180 degree end cell row cell sin invisible function application 180 degree end cell cell cos invisible function application 180 degree end cell end table close parentheses open parentheses table row cell 6 minus 2 end cell row cell negative 2 plus 1 end cell end table close parentheses  open parentheses table row cell x to the power of apostrophe minus 2 end cell row cell y to the power of apostrophe plus 1 end cell end table close parentheses equals open parentheses table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses open parentheses table row 4 row cell negative 1 end cell end table close parentheses  open parentheses table row cell x to the power of apostrophe minus 2 end cell row cell y to the power of apostrophe plus 1 end cell end table close parentheses equals open parentheses table row cell negative 4 end cell row 1 end table close parentheses  D i d a p a t  x to the power of apostrophe minus 2 equals negative 4 left right double arrow x to the power of apostrophe equals negative 2  y to the power of apostrophe plus 1 equals 1 left right double arrow y to the power of apostrophe equals 0  M a k a space B to the power of apostrophe left parenthesis negative 2 comma 0 right parenthesis    T i t i k space C left parenthesis 5 comma 2 right parenthesis  open parentheses table row cell x to the power of apostrophe minus 2 end cell row cell y to the power of apostrophe plus 1 end cell end table close parentheses equals open parentheses table row cell cos invisible function application 180 degree end cell cell negative sin invisible function application 180 degree end cell row cell sin invisible function application 180 degree end cell cell cos invisible function application 180 degree end cell end table close parentheses open parentheses table row cell 5 minus 2 end cell row cell 2 plus 1 end cell end table close parentheses  open parentheses table row cell x to the power of apostrophe minus 2 end cell row cell y to the power of apostrophe plus 1 end cell end table close parentheses equals open parentheses table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses open parentheses table row 3 row 3 end table close parentheses  open parentheses table row cell x to the power of apostrophe minus 2 end cell row cell y to the power of apostrophe plus 1 end cell end table close parentheses equals open parentheses table row cell negative 3 end cell row cell negative 3 end cell end table close parentheses  D i d a p a t  x to the power of apostrophe minus 2 equals negative 3 left right double arrow x to the power of apostrophe equals negative 1  y to the power of apostrophe plus 1 equals negative 3 left right double arrow y to the power of apostrophe equals negative 4  M a k a space A to the power of apostrophe left parenthesis negative 1 comma negative 4 right parenthesis

Jawaban terverifikasi

Dijawab oleh:

Y. Endah

Mahasiswa/Alumni Institut Teknologi Bandung

Terakhir diupdate 04 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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