Points A and B are at $(8 ,3 )$ and $(1 ,4 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ 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 $(8 ,3 )$ and $(1 ,4 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ 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 · 2018-02-15T21:02:44

$C=(-3,8)$

Explanation:

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

$• " a point "(x,y)to(-y,x)$

$rArrA(8,3)toA'(-3,8)" where A' is the image of A"$

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

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

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

$rArrulc=2ula'-ulb$

$color(white)(rArrulc)=2((-3),(8))-((-3),(8))$

$color(white)(rArrulc)=((-6),(16))-((-3),(8))=((-3),(8))$

$rArrC=(-3,8)$

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Points A and B are at $(8 ,3 )$ and $(1 ,4 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ 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?

1 Answer

Explanation:

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Humanities

... and beyond

Points A and B are at (8 ,3 )(8 ,3 ) and (1 ,4 )(1 ,4 ), respectively. Point A is rotated counterclockwise about the origin by pi/2 pi/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 $(8 ,3 )$ and $(1 ,4 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ 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?