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
Jim G.
Jun 10, 2018

#C=(-7,10)#

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)#

Related questions
See all questions in Dilations or Scaling around a Point
Impact of this question
1116 views around the world
You can reuse this answer
Creative Commons License