Points A and B are at $(4 ,9 )$ and $(7 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $(3pi)/2$ and dilated about point C by a factor of $1/2$ . 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 $(4 ,9 )$ and $(7 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $(3pi)/2$ and dilated about point C by a factor of $1/2$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2018-01-24T20:01:48

$C=(5,14)$

Explanation:

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

$• " a point "(x,y)to(y,-x)$

$rArrA(4,9)toA'(9,-4)" where A' is the image of A"$

$rArrvec(CB)=color(red)(1/2)vec(CA')$

$rArrulb-ulc=1/2(ula'-ulc)=1/2ula'-1/2ulc$

$rArr-1/2ulc=1/2a'-ulb$

$color(white)(xxxxxx)=1/2((9),(-4))-((7),(5))=((-5/2),(-7))$

$rArrulc=-2((-5/2),(-7))=((5),(14))$

$rArrC=(5,14)$

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Points A and B are at $(4 ,9 )$ and $(7 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $(3pi)/2$ and dilated about point C by a factor of $1/2$ . 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 (4 ,9 )(4 ,9 ) and (7 ,5 )(7 ,5 ), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 (3pi)/2 and dilated about point C by a factor of 1/2 1/2 . 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 $(4 ,9 )$ and $(7 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $(3pi)/2$ and dilated about point C by a factor of $1/2$ . If point A is now at point B, what are the coordinates of point C?