# Points A and B are at #(3 ,7 )# and #(4 ,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

After Point A is rotated counterclockwise about the origin by

The difference between the

Since Point A was dilated about Point C by a factor of 5, we can find out by how much the coordinates change with each integer increase in factor.

For the

and

So for every integer increase in factor, the point moves 1.75 to the right and 2.25 upwards.

Point C is therefore

#### Explanation:

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

#• " a point "(x,y)to(-x,-y)#

#rArrA(3,7)toA'(-3,-7)" 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)(4ulcxx)=5((-3),(-7))-((4),(2))#

#color(white)(xxxx)=((-15),(-35))-((4),(2))=((-19),(-37))#

#rArrulc=1/4((-19),(-37))=((-19/4),(-37/4))#

#rArrC=(-19/4,-37/4)#