Points A and B are at #(4 ,3 )# and #(1 ,4 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #2 #. If point A is now at point B, what are the coordinates of point C?
1 Answer
Jun 16, 2017
Explanation:
#"under a clockwise rotation about the origin of " pi/2#
#• " a point " (x,y)to(-y,x)#
#rArrA(4,3)toA'(-3,4)" where A' is the image of A"#
#"under a dilatation about C of factor 2"#
#vec(CB)=2vec(CA')#
#rArrulb-ulc=2(ula'-ulc)#
#rArrulb-ulc=2ula'-2ulc#
#rArrulc=2ula'-ulb#
#color(white)(rArrulc)=2((-3),(4))-((1),(4))#
#color(white)(rArrulc)=((-6),(8))-((1),(4))=((-7),(4))#
#rArrC=(-7,4)#
