Points A and B are at (4 ,1 ) and (7 ,5 ), respectively. Point A is rotated counterclockwise about the origin by pi/2 and dilated about point C by a factor of 1/2 . If point A is now at point B, what are the coordinates of point C?

1 Answer
Jim G.
May 23, 2018

C=(15/4,7/2)

Explanation:

"under a counterclockwise rotation about the origin of "pi/2

• " a point "(x,y)to(-y,x)

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

vec(CB)=color(red)(1/2)vec(CA')

"expressing in terms of position vectors gives"

ulb-ulc=1/2(ula'-ulc)

ulb-ulc=1/2ula'-1/2ulc

1/2ulc=ulb-1/2ula'

color(white)(1/2ulc)=((7),(5))-1/2((-1),(4))

color(white)(1/2ulc)=((7),(5))-((-1/2),(-2))=((15/2),(7))

ulc=1/2((15/2),(7))=((15/4),(7/2))

"thus "C=(15/4,7/2)

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