Points A and B are at (4 ,1 )(4,1) and (5 ,9 )(5,9), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 3π2 and dilated about point C by a factor of 4 4. If point A is now at point B, what are the coordinates of point C?

1 Answer
Jim G.
Apr 12, 2018

C=(-1/3,-25/3)C=(−13,−253)

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(4,1)toA'(1,-4)" where A' is the image of A"

rArrvec(CB)=color(red)(4)vec(CA')

rArrulb-ulc=4(ula'-ulc)

rArrulb-ulc=4ula'-4ulc

rArr3ulc=4ula'-ulb

color(white)(rArr3ulc)=4((1),(-4))-((5),(9))

color(white)(rArr3ulc)=((4),(-16))-((5),(9))=((-1),(-25))

rArrulc=1/3((-1),(-25))=((-1/3),(-25/3))

rArrC=(-1/3,-25/3)

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