Points A and B are at #(3 ,7 )# and #(2 ,4 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/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
Jun 30, 2018

Answer:

#C=(-10,8/3)#

Explanation:

#"under a counterclockwise rotation about the origin of "pi/2#

#• " a point "(x,y)to(-y,x)#

#A(3,7)toA'(-7,3)" where A' is the image of A"#

#vec(CB)=color(red)(4)vec(CA')#

#ulb-ulc=4(ula'-ulc)#

#ulb-ulc=4ula'-4ulc#

#3ulc=4ula'-ulb#

#color(white)(3ulc)=4((-7),(3))-((2),(4))#

#color(white)(3ulc)=((-28),(12))-((2),(4))=((-30),(8))#

#ulc=1/3((-30),(8))=((-10),(8/3))#

#rArrC=(-10,8/3)#