Points A and B are at (9 ,3 )(9,3) and (7 ,8 )(7,8), 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.
Jul 22, 2018

C=(-17,-17/2)C=(−17,−172)

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)

A(9,3)toA'(-9,-3)" where A' is the image of A"

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

ulb-ulc=3(ula'-ulc)

ulb-ulc=3ula'-3ulc

2ulc=3ula'-ulb

color(white)(2ulc)=3((-9),(-3))-((7),(8))

color(white)(2ulc)=((-27),(-9))-((7),(8))=((-34),(-17))

ulc=1/2((-34),(-17))=((-17),(-17/2))

rArrC=(-17,-17/2)

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