Points A and B are at $(5 ,7 )$ and $(3 ,6 )$ , 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 $(5 ,7 )$ and $(3 ,6 )$ , 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 · 2018-05-22T06:54:41

$C=(-13,-20)$

Explanation:

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

$• " a point "(x,y)to(-x,-y)$

$rArrA(5,7)toA'(-5,-7)" where A' is the image of A"$

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

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

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

$rArrulc=2ula'-ulb$

$color(white)(rArrulc)=2((-5),(-7))-((3),(6))$

$color(white)(rArrulc)=((-10),(-14))-((3),(6))=((-13),(-20))$

$rArrC=(-13,-20)$

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Points A and B are at $(5 ,7 )$ and $(3 ,6 )$ , 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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Science

Math

Humanities

... and beyond

Points A and B are at (5 ,7 )(5 ,7 ) and (3 ,6 )(3 ,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 $(5 ,7 )$ and $(3 ,6 )$ , 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?