Points A and B are at #(4 ,6 )# and #(7 ,5 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #5 #. If point A is now at point B, what are the coordinates of point C?
2 Answers
Explanation:
Rotating Point A counterclockwise by
The distance between
The distance between A' and B must be five times the distance between A' and C
The vector to go from B to A' is
1/4 of that vector is
Apply that to A' to get
Explanation:
#"under a counterclockwise rotation about the origin of "pi/2#
#• " a point "(x,y)to(-y,x)#
#rArrA(4,6)toA'(-6,4)" where A' is the image of A"#
#rArrvec(CB)=color(red)(5)vec(CA')#
#rArrulb-ulc=5(ula'-ulc)#
#rArrulb-ulc=5ula'-5ulc#
#rArr4ulc=5ula'-ulb#
#color(white)(rArr4ulc)=5((-6),(4))-((7),(5))#
#color(white)(rArrulc)=((-30),(20))-((7),(5))=((-37),(15))#
#rArrulc=1/4((-37),(15))=((-37/4),(15/4))#
#rArrC=(-37/4,15/4)#