Points A and B are at #(3 ,7 )# and #(6 ,1 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/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 15, 2017
Explanation:
#"under a counterclockwise rotation about the origin of "pi/2#
#• " a point "(x,y)to(-y,x)#
#rArra(3,7)toA'(-7,3)" 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)(2ulcxxx)=3((-7),(3))-((6),(1))#
#color(white)(xxxxx)=((-21),(9))-((6),(1))=((-27),(8))#
#rArrulc=1/2((-27),(8))=((-27/2),(4))#
#rArrC=(-27/2,4)#
