Points A and B are at (7 ,1 )(7,1) and (3 ,7 )(3,7), respectively. Point A is rotated counterclockwise about the origin by pi π 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
Jim G.
Apr 20, 2018

C=(-12,-5)C=(−12,−5)

Explanation:

"under a counterclockwise rotation about the origin of "piunder a counterclockwise rotation about the origin of π

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

rArrA(7,1)toA'(-7,-1)" 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((-7),(-1))-((3),(7))

color(white)(rArr2ulc)=((-21),(-3))-((3),(7))=((-24),(-10))

rArrulc=1/2((-24),(-10))=((-12),(-5))

rArrC=(-12,-5)

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