Points A and B are at (3 ,5 ) and (6 ,5 ), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 and dilated about point C by a factor of 3 . If point A is now at point B, what are the coordinates of point C?

1 Answer
Apr 1, 2018

C=(9/2,-7)

Explanation:

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

• " a point "(x,y)to(y,-x)

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

color(white)(rArr2ulc)=((15),(-9))-((6),(5))=((9),(-14))

rArrulc=1/2((9),(-14))=((9/2),(-7))

rArrC=(9/2,-7)