Points A and B are at $(7 ,3 )$ and $(5 ,9 )$ , respectively. Point A is rotated counterclockwise about the origin by $(3pi)/2$ and dilated about point C by a factor of $2$ . 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 $(7 ,3 )$ and $(5 ,9 )$ , respectively. Point A is rotated counterclockwise about the origin by $(3pi)/2$ and dilated about point C by a factor of $2$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2018-06-21T10:25:49

$C=(1,-23)$

Explanation:

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

$• " a point "(x,y)to(y,-x)$

$A(7,3)toA'(3,-7)$

$vec(CB)=color(red)(2)vec(CA')$

$ulb-ulc=2(ula'-ulc)$

$ulb-ulc=2ula'-2ulc$

$ulc=2ula'-ulb$

$color(white)(ulc)=2((3),(-7))-((5),(9))$

$color(white)(ulc)=((6),(-14))-((5),(9))=((1),(-23))$

$rArrC=(1,-23)$

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Points A and B are at $(7 ,3 )$ and $(5 ,9 )$ , respectively. Point A is rotated counterclockwise about the origin by $(3pi)/2$ and dilated about point C by a factor of $2$ . If point A is now at point B, what are the coordinates of point C?

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Explanation:

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Points A and B are at (7 ,3 )(7 ,3 ) and (5 ,9 )(5 ,9 ), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 (3pi)/2 and dilated about point C by a factor of 2 2 . 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 $(7 ,3 )$ and $(5 ,9 )$ , respectively. Point A is rotated counterclockwise about the origin by $(3pi)/2$ and dilated about point C by a factor of $2$ . If point A is now at point B, what are the coordinates of point C?