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

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Answer 1 · 2018-05-28T14:37:11

$C=(7/2,-13)$

Explanation:

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

$• " a point "(x,y)to(y,-x)$

$A(8,5)toA'(5,-8)" where A' is the image of A"$

$vec(CB)=color(red)(3)vec(CA')$

$ulb-ulc=3(ula'-ulc)$

$ulb-ulc=3ula'-3ulc$

$2ulc=3ula'-ulb$

$color(white)(2ulc)=3((5),(-8))-((8),(2))$

$color(white)(2ulc)=((15),(-24))-((8),(2))=((7),(-26))$

$ulc=1/2((7),(-26))=((7/2),(-13))$

$rArrC=(7/2,-13)$

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