Points A and B are at (2 ,9 ) and (8 ,7 ), respectively. Point A is rotated counterclockwise about the origin by (3pi)/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
Jim G.
Feb 11, 2018

C=(19/2,-13/2)

Explanation:

"under a counterclockwise rotation about the origin of "(3pi)/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))-((8),(7))

color(white)(rArr2ulc)=((27),(-6))-((8),(7))=((19),(-13))

rArrulc=1/2((19),(-13))=((19/2),(-13/2))

rArrC=(19/2,-13/2)

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