Points A and B are at $(5 ,8 )$ and $(8 ,1 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ and dilated about point C by a factor of $4$ . 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 $(5 ,8 )$ and $(8 ,1 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ and dilated about point C by a factor of $4$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2018-01-14T14:24:14

$C=(-40/3,-7)$

Explanation:

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

$• " a point "(x,y)to(-x-y)$

$rArrA(5,8)toA'(-8,-5)" where A' is the image of A"$

$rArrvec(CB)=color(red)(4)vec(CA')$

$rArrulb-ulc=4(ula'-ulc)$

$rArrulb-ulc=4ula'-4ulc$

$rArr3ulc=4ula'-ulb$

$color(white)(rArrul3c)=4((-8),(-5))-((8),(1))$

$color(white)(rArrul3c)=((-32),(-20))-((8),(1))=((-40),(-21))$

$rArrulc=1/3((-40),(-21))=((-40/3),(-7))$

$rArrC=(-40/3,-7)$

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Points A and B are at $(5 ,8 )$ and $(8 ,1 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ and dilated about point C by a factor of $4$ . If point A is now at point B, what are the coordinates of point C?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

Points A and B are at (5 ,8 )(5 ,8 ) and (8 ,1 )(8 ,1 ), respectively. Point A is rotated counterclockwise about the origin by pi pi and dilated about point C by a factor of 4 4 . 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 $(5 ,8 )$ and $(8 ,1 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ and dilated about point C by a factor of $4$ . If point A is now at point B, what are the coordinates of point C?