Points A and B are at $(5 ,9 )$ and $(8 ,6 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ 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 $(5 ,9 )$ and $(8 ,6 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ 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 · 2018-07-26T12:28:36

$C=(-18,-24)$

Explanation:

$"Under a counterclockwise rotation about the origin of "pi$

$• " a point "(x,y)to(-x,-y)$

$A(5,9)toA'(-5,-9)" where A' is the image of A"$

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

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

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

$ulc=2ula'-ulb$

$color(white)(ulc)=2((-5),(-9))-((8),(6))$

$color(white)(ulc)=((-10),(-18))-((8),(6))=((-18),(-24))$

$rArrC=(-18,-24)$

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Points A and B are at $(5 ,9 )$ and $(8 ,6 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ 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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Math

Humanities

... and beyond

Points A and B are at (5 ,9 )(5 ,9 ) and (8 ,6 )(8 ,6 ), respectively. Point A is rotated counterclockwise about the origin by pi pi 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 $(5 ,9 )$ and $(8 ,6 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ 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?