Points A and B are at #(3 ,7 )# and #(7 ,2 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # 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
The point
Explanation:
The point
The coordinates of
Let the point
Then,
Therefore,
So,
and
Therefore,
The point
Explanation:
Under a counterclockwise rotation about the origin of
#pi#
#• "a point " (x,y)to(-x,-y)#
#" Under a dilatation about C of factor 5"# Taking a
#color(blue)"vector approach"#
#rArrvec(CB)=5vec(CA')#
#rArrulb-ulc=5(ula'-ulc)#
#rArrulb-ulc=5ula'-5ulc#
#rArr4ulc=5ula'-ulb#
#color(white)(rArr4c)=5((-3),(-7))-((7),(2))#
#color(white)(rArr4c)=((-15),(-35))-((7),(2))#
#color(white)(rArr4c)=((-22),(-37))#
#rArrulc=1/4((-22),(-37))=((-11/2),(-37/4))#
#rArrC=(-11/2,-37/4)#