Points A and B are at #(8 ,3 )# and #(5 ,4 )#, 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
Jun 10, 2018
Explanation:
#"under a counterclockwise rotation about the origin of "pi/2#
#• " a point "(x,y)to(-y,x)#
#A(8,3)toA'(-3,8)" where A' is the image of A"#
#vec(CB)=color(red)(3)vec(CA')#
#ulb-ulc=3(ula'-ulc)#
#ulb-ulc=3ula'-3ulc#
#2ulc=3ula'-ulb#
#color(white)(2ulc)=3((-3),(8))-((5),(4))#
#color(white)(2ulc)=((-9),(24))-((5),(4))=((-14),(20))#
#ulc=1/2((-14),(20))=((-7),(10))#
#rArrC=(-7,10)#
