Points A and B are at #(2 ,9 )# and #(3 ,2 )#, 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
Jun 5, 2017
Explanation:
#"Under a counterclockwise rotation about the origin of "pi/2#
#• " a point " (x,y)to(-y,x)#
#rArrA(2,9)toA'(-9,2)" where " A' " is the image of A"#
#"Under a dilatation about " C" of factor 3"#
#vec(CB)=color(red)(3)vec(CA')#
#rArrulb-ulc=color(red)(3)(ula'-ulc)#
#rArrulb-ulc=3ula'-3ulc#
#rArr2ulc=3ula'-ulb#
#color(white)(rArr2cx)=3((-9),(2))-((3),(2))=((-30),(4))#
#rArrulc=1/2((-30),(4))=((-15),(2))#
#rArrC=(-15,2)#
