Points A and B are at #(6 ,5 )# and #(3 ,8 )#, 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?

2 Answers
sankarankalyanam
Jun 8, 2018

#color(green)("Coordinates of " C = (-13,4)#

Explanation:

#A (6,5), B(3,8), " rotated counter clockwise by " pi/2 " and dilated by factor 2"#

Coordinates of A after #pi/2# counter clockwise rotation is

#A(6,5) -> A'(-5,6)#

#vec(BC) = 2 vec(A'C)#

#b - c = 2 (a' - c)#

#c = 2a' - b#

#C((x),(y)) = 2 ((-5),(6)) - ((3),(8)) =color(green)( ((-13),(4))#

Jim G.
Jun 8, 2018

#C=(-13,4)#

Explanation:

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

#• " a point "(x,y)to(-y,x)#

#A(6,5)toA'(-5,6)" where A' is the image if A"#

#vec(CB)=color(red)(2)vec(CA')#

#ulb-ulc=2(ula'-ulc)#

#ulb-ulc=2ula'-2ulc#

#ulc=2ula'-ulb#

#color(white)(ulc)=2((-5),(6))-((3),(8))#

#color(white)(ulc)=((-10),(12))-((3),(8))=((-13),(4))#

#rArrC=(-13,4)#

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