Points A and B are at $(9 ,3 )$ and $(7 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ and dilated about point C by a factor of $3$ . 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 $(9 ,3 )$ and $(7 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ and dilated about point C by a factor of $3$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2018-07-22T13:27:19

$C=(-17,-17/2)$

Explanation:

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

$• " a point "(x,y)to(-x,-y)$

$A(9,3)toA'(-9,-3)" where A' is the image of A"$

$vec(CB)=color(red)(3)vec(CA')$

$ulb-ulc=3(ula'-ulc)$

$ulb-ulc=3ula'-3ulc$

$2ulc=3ula'-ulb$

$color(white)(2ulc)=3((-9),(-3))-((7),(8))$

$color(white)(2ulc)=((-27),(-9))-((7),(8))=((-34),(-17))$

$ulc=1/2((-34),(-17))=((-17),(-17/2))$

$rArrC=(-17,-17/2)$

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Points A and B are at $(9 ,3 )$ and $(7 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ and dilated about point C by a factor of $3$ . 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 (9 ,3 )(9 ,3 ) and (7 ,8 )(7 ,8 ), respectively. Point A is rotated counterclockwise about the origin by pi pi and dilated about point C by a factor of 3 3 . 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 $(9 ,3 )$ and $(7 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ and dilated about point C by a factor of $3$ . If point A is now at point B, what are the coordinates of point C?