Points A and B are at $(7 ,1 )$ and $(7 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ 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 $(7 ,1 )$ and $(7 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ 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 · 2018-02-24T20:15:36

$C=(15,3)$

Explanation:

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

$• " a point "(x,y)to(-y,x)$

$rArrA(7,1)toA'(-1,7)" where A' is the image of A"$

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

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

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

$rArr1/2ulc=ulb-1/2ula'$

$color(white)(rArr1/2ulc)=((7),(5))-1/2((-1),(7))=((15/2),(3/2))$

$rArrulc=2((15/2),(3/2))=((15),(3))$

$rArrC=(15,3)$

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Points A and B are at $(7 ,1 )$ and $(7 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ 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 (7 ,1 )(7 ,1 ) and (7 ,5 )(7 ,5 ), respectively. Point A is rotated counterclockwise about the origin by pi/2 pi/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 $(7 ,1 )$ and $(7 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ 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?