Points A and B are at $(4 ,5 )$ and $(6 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $(3pi)/2$ and dilated about point C by a factor of $4$ . If point A is now at point B, what are the coordinates of point C?

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Points A and B are at $(4 ,5 )$ and $(6 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $(3pi)/2$ and dilated about point C by a factor of $4$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2018-07-29T13:05:33

$C=(14/3,-8)$

Explanation:

$"under a counterclockwise rotation about the origin of "(3pi)/2$

$• " a point "(x,y)to(y,-x)$

$A(4,5)toA'(5,-4)" where A' is the image of A"$

$vec(CB)=color(red)(4)vec(CA')$

$ulb-ulc=4(ula'-ulc)$

$ulb-ulc=4ula'-4ulc$

$3ulc=4ula'-ulb$

$color(white)(3ulc)=4((5),(-4))-((6),(8))$

$color(white)(3ulc)=((20),(-16))-((6),(8))=((14),(-24))$

$ulc=1/3((14),(-24))=((14/3),(-8))$

$rArrC=(14/3,-8)$

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Points A and B are at $(4 ,5 )$ and $(6 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $(3pi)/2$ and dilated about point C by a factor of $4$ . If point A is now at point B, what are the coordinates of point C?

1 Answer

Explanation:

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Points A and B are at (4 ,5 )(4 ,5 ) and (6 ,8 )(6 ,8 ), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 (3pi)/2 and dilated about point C by a factor of 4 4 . If point A is now at point B, what are the coordinates of point C?

1 Answer

Explanation:

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Points A and B are at $(4 ,5 )$ and $(6 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $(3pi)/2$ and dilated about point C by a factor of $4$ . If point A is now at point B, what are the coordinates of point C?