# Points A and B are at #(7 ,9 )# and #(6 ,2 )#, 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 image of

#### Explanation:

I don't get why these come up as recently asked when they're two years old.

The image of rotating

Let's see where a point D ends up after dilation around C by a factor of

That is always interesting to me. It's the parametric equation for a line between C (

We have

Check:

#### Explanation:

#• " a point "(x,y)to(y,-x)#

#rArrA(7,9)toA'(9,-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((9),(-7))-((6),(2))#

#color(white)(rArrulc)=((18),(-14))-((6),(2))=((12),(-16))#

#rArrC=(12,-16)#