Points A and B are at (8 ,5 ) and (2 ,3 ), 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
Aug 17, 2017
Explanation:
"under a counterclockwise rotation about the origin of "(3pi)/2
• " a point "(x,y)to(y,-x)
rArrA(8,5)toA'(5,-8)" where A' is the image of A"
"under a dilatation about C of factor 3"
vec(CB)=color(red)(3)vec(CA')
rArrulb-ulc=color(red)(3)(ula'-ulc)
rArrulb-ulc=3ula'-3ulc
rArr2ulc=3ula'-ulb
color(white)(xxxx)=3((5),(-8))-((2),(3))
color(white)(xxxx)=((15),(-24))-((2),(3))=((13),(-27))
rArrulc=1/2((13),(-27))=((13/2),(-27/2))
rArrC=(13/2,-27/2)
