Points A and B are at #(2 ,7 )# and #(4 ,6 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # 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
Mar 21, 2018

#C=(-5,-27/2)#

Explanation:

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

#• " a point "(x,y)to(-x,-y)#

#rArrA(2,7)toA'(-2,-7)" 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((-2),(-7))-((4),(6))#

#color(white)(rArr2ulc)=((-6),(-21))-((4),(6))=((-10),(-27))#

#rArrulc=1/2((-10),(-27))=((-5),(-27/2))#

#rArrC=(-5,-27/2)#