Points A and B are at (4 ,1 ) and (3 ,9 ), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 and dilated about point C by a factor of 4 . If point A is now at point B, what are the coordinates of point C?
1 Answer
May 11, 2018
Explanation:
"under a counterclockwise rotation about the origin of "(3pi)/2
• " a point "(x,y)to(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))-((3),(9))
color(white)(rArr3ulc)=((4),(-16))-((3),(9))=((1),(-25))
rArrulc=1/3((1),(-25))=((1/3),(-25/3))
rArrC=(1/3,-25/3)
