Points A and B are at $(2 ,9 )$ and $(3 ,1 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ 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 $(2 ,9 )$ and $(3 ,1 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ 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 · 2018-05-15T10:39:52

$C=(-15,5/2)$

Explanation:

$"under a counterclockwise rotation about the origin of "pi/2$

$• " a point "(x,y)to(-y,x)$

$rArrA(2,9)toA'(-9,2)" where A' is the image of A"$

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

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

$rArrulb-ulc=3ula'-3ulc$

$rArr2ulc=3ula'-ulb$

$color(white)(rArr2ulc)=3((-9),(2))-((3),(1))$

$color(white)(rArr2ulc)=((-27),(6))-((3),(1))=((-30),(5))$

$rArrulc=1/2((-30),(5))=((-15),(5/2))$

$rArrC=(-15,5/2)$

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Points A and B are at $(2 ,9 )$ and $(3 ,1 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ 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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Science

Math

Humanities

... and beyond

Points A and B are at (2 ,9 )(2 ,9 ) and (3 ,1 )(3 ,1 ), respectively. Point A is rotated counterclockwise about the origin by pi/2 pi/2 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 $(2 ,9 )$ and $(3 ,1 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ 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?