Lingkaran didilatasikan dengan faktor skala terh...

Lingkaran $begin mathsize 14px style straight L colon space left parenthesis x minus 1 right parenthesis squared plus left parenthesis y plus 1 right parenthesis squared equals 9 end style$ didilatasikan dengan faktor skala $begin mathsize 14px style 1 third end style$ terhadap titik pusat $begin mathsize 14px style left parenthesis 1 comma space 2 right parenthesis end style$ . Hasil dilatasi lingkaran $begin mathsize 14px style straight L end style$ adalah . . . .

$begin mathsize 14px style left parenthesis x plus 1 right parenthesis squared plus left parenthesis y plus 1 right parenthesis squared equals 1 end style$
$begin mathsize 14px style left parenthesis x plus 1 right parenthesis squared plus left parenthesis y minus 1 right parenthesis squared equals 1 end style$
$begin mathsize 14px style left parenthesis x minus 1 right parenthesis squared plus left parenthesis y minus 1 right parenthesis squared equals 1 end style$
$begin mathsize 14px style left parenthesis x minus 2 right parenthesis squared plus left parenthesis y plus 2 right parenthesis squared equals 1 end style$
$begin mathsize 14px style left parenthesis x plus 2 right parenthesis squared plus left parenthesis y minus 2 right parenthesis squared equals 1 end style$

Jawaban:

$begin mathsize 14px style left parenthesis x minus a right parenthesis squared plus open parentheses y minus b close parentheses squared equals r left parenthesis x minus 1 right parenthesis plus open parentheses y plus 1 close parentheses squared equals 9 squared end style$

Koordinat titik pusat lingkaran adalah $begin mathsize 14px style left parenthesis 1 comma negative 1 right parenthesis end style$ , akan didilatasikan dengan faktor skala $begin mathsize 14px style 1 third end style$ terhadap titik pusat $begin mathsize 14px style left parenthesis 1 comma space 2 right parenthesis end style$ :

$begin mathsize 14px style open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses equals open parentheses table row k 0 row 0 k end table close parentheses open parentheses table row cell x minus a end cell row cell y minus b end cell end table close parentheses plus open parentheses table row a row b end table close parentheses space space space space space space space space equals open parentheses table row cell 1 third end cell 0 row 0 cell 1 third end cell end table close parentheses open parentheses table row cell 1 minus 1 end cell row cell negative 1 minus 2 end cell end table close parentheses plus open parentheses table row 1 row 2 end table close parentheses space space space space space space space space equals open parentheses table row cell 1 third end cell 0 row 0 cell 1 third end cell end table close parentheses open parentheses table row 0 row cell negative 3 end cell end table close parentheses plus open parentheses table row 1 row 2 end table close parentheses space space space space space space space space equals open parentheses table row 0 row cell negative 1 end cell end table close parentheses plus open parentheses table row 1 row 2 end table close parentheses space space space space space space space space equals open parentheses table row 1 row 1 end table close parentheses end style$

Hasil dilatasi lingkaran $begin mathsize 14px style straight L end style$ adalah

$begin mathsize 14px style left parenthesis x minus a right parenthesis squared plus open parentheses y minus b close parentheses squared equals r left parenthesis x minus 1 right parenthesis squared plus open parentheses y minus 1 close parentheses squared equals r end style$

Jadi, jawaban yang tepat adalah C.

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