Points A and B are at #(3 ,5 )# 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
Mar 21, 2018

#C=(-21/2,4)#

Explanation:

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

.#• " a point "(x,y)to(-y,x)#

#rArrA(3,5)toA'(-5,3)" 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((-5),(3))-((6),(1))#

#color(white)(rArr2ulc)=((-15),(9))-((6),(1))=((-21),(8))#

#rArrulc=1/2((-21),(8))=((-21/2),(4))#

#rArrC=(-21/2,4)#