Pertanyaan

Diketahui gradien garis yang melalui titik O (0,0) dan P(a,b) adalah 3. Jika P dicerminkan terhadap sumbu y kemudian digeser 1 satuan ke atas dan 4 satuan ke kiri, maka gradien garis yang melalui P' dan O (0,0) adalah -1. Titik P adalah...

(-2,-4)
(-1,-2)
(1,2)
(2,4)
(3,6)

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Klaim

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

$G r a d i e n space g a r i s space y a n g space m e l a l u i space t i t i k space P left parenthesis a comma b right parenthesis space d a n space O left parenthesis 0 comma 0 right parenthesis space a d a l a h space 2 space m a k a space fraction numerator b minus 0 over denominator a minus 0 end fraction equals 2 left right double arrow b equals 2 a P left parenthesis a comma b right parenthesis space D i c e r m i n k a n space t e r h a d a p space s u m b u space y space colon space P left parenthesis negative a comma b right parenthesis K e m u d i a n space t i t i k space t e r s e b u t space d i g e s e r space 1 space s a t u a n space k e space a t a s space d a n space 4 space s a t u a n space k e space k i r i space m a k a space h a s i ln y a space a d a l a h P apostrophe left parenthesis negative a minus 4 comma b plus 1 right parenthesis space K e m u d i a n space g r a d i e n space g a r i s space y a n g space m e l a l u i space t i t i k space O left parenthesis 0 comma 0 right parenthesis space d a n space P to the power of apostrophe left parenthesis negative a minus 4 comma b plus 1 right parenthesis space a d a l a h space minus 1 space m a k a minus 1 equals fraction numerator b plus 1 minus 0 over denominator negative a minus 4 minus 0 end fraction b plus 1 equals a plus 4 b minus a equals 3 space horizontal ellipsis. left parenthesis 2 right parenthesis S u b t i t u s i k a n space p e r s a m a a n space left parenthesis 1 right parenthesis space k e space p e r s a m a a n space left parenthesis 2 right parenthesis 2 a minus a equals 3 space a equals 3 space b minus 3 equals 3 left right double arrow b equals 6 space M a k a space P left parenthesis a comma b right parenthesis equals P left parenthesis 3 comma 6 right parenthesis$