Points A and B are at #(5 ,7 )# and #(3 ,6 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # 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?

Answer 1

Sadie Allen

#C=(-13,-20)#

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

#• " a point "(x,y)to(-x,-y)#

#rArrA(5,7)toA'(-5,-7)" where A' is the image of A"#

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

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

#rArrulb-ulc=2ula'-2ulc#

#rArrulc=2ula'-ulb#

#color(white)(rArrulc)=2((-5),(-7))-((3),(6))#

#color(white)(rArrulc)=((-10),(-14))-((3),(6))=((-13),(-20))#

#rArrC=(-13,-20)#

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Answer 2

Jayden Jackson

The coordinates of point C are (-1, 5).

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