Points A and B are at (6 ,1 )(6,1) and (3 ,5 )(3,5), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 3π2 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
Jim G.
Apr 22, 2018

C=(-1,-17)C=(−1,−17)

Explanation:

"under a counterclockwise rotation about the origin of "(3pi)/2under a counterclockwise rotation about the origin of 3π2

• " a point "(x,y)to(y,-x)∙ a point (x,y)→(y,−x)

rArrA(6,1)toA'(1,-6)" 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((1),(-6))-((3),(5))

color(white)(rArrulc)=((2),(-12))-((3),(5))=((-1),(-17))

rArrC=(-1,-17)

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