Points A and B are at (8 ,9 )(8,9) and (8 ,2 )(8,2), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 3π2 and dilated about point C by a factor of 3 3. If point A is now at point B, what are the coordinates of point C?
1 Answer
Feb 6, 2018
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(8,9)toA'(9,-8)" 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((9),(-8))-((8),(2))
color(white)(rArr2ulc)=((27),(-24))-((8),(2))=((19),(-26))
rArrulc=1/2((19),(-26))=((19/2),(-13))
rArrC=(19/2,-13)
