# Points A and B are at #(1 ,1 )# and #(4 ,6 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/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

The point

#### Explanation:

First, rotate

A 270º rotation is three-fourths of a circle, so the point

Now, we can figure out the equation on the line between

Since the dilation from point

The change in

We now know that the

We can plug in -2 to our line that we found to get the

Therefore, the point

#### Explanation:

#"under a counterclockwise rotation about the origin of "(3pi)/2#

#• " a point "(x,y)to(y,-x)#

#rArra(1,1)toA'(1,-1)" 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((1),(-1))-((4),(6))#

#color(white)(rArrulc)=((2),(-2))-((4),(6))=((-2),(-8))#

#rArrC=(-2,-8)#