Points A and B are at $(2 ,7 )$ and $(8 ,6 )$ , 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 $(2 ,7 )$ and $(8 ,6 )$ , 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 · 2018-02-22T21:28:46

$C=(-16/3,-34/3)$

Explanation:

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

$• " a point "(x,y)to(-x,-y)$

$rArrA(2,7)toA'(-2,-7)" where A' is the image of A"$

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

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

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

$rArr3ulc=4ula'-ulb$

$color(white)(rArr3ulc)=4((-2),(-7))-((8),(6))$

$color(white)(rArr3ulc)=((-8),(-28))-((8),(6))=((-16),(-34))$

$rArrulc=1/3((-16),(-34))=((-16/3),(-34/3))$

$rArrC=(-16/3,-34/3)$

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Points A and B are at $(2 ,7 )$ and $(8 ,6 )$ , 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 (2 ,7 )(2 ,7 ) 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 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 $(2 ,7 )$ and $(8 ,6 )$ , 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?