# Points A and B are at #(4 ,5 )# and #(7 ,2 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #1/2 #. If point A is now at point B, what are the coordinates of point C?

##### 1 Answer

#### Explanation:

Given:

Required: the coordinates of C such that

Solution Strategy: a) Rotate

b) Using Dilation about a

a) Rotation of

b) In order to dilate about C(x,y) we need to do do the following:

i) Translation

ii) Dilate by 1/2,

iii) Undo the translation:

Putting i), ii) and iii) we can wrtite: