Question

With the origin as the center of dilation, rectangle pqrs will be dilated by a scale factor of 1/3 to form rectangle pqrs'. what will be the new coordinates for point q'

Answer 1

For a dilation centered around the origin   
Dk (x,y) = (kx, ky)   
So let's say you have a rectangle PQRS where 
P = (0,0)
 Q = (4,0)
 R = (4,4)
 S = (0,4)  
 To get the dilation of this PQRS to P'Q'R'S' with scale factor 1/4 you multiply every coordinate by 1/4.   
 P' = (0.0)
 Q' = (1,0)
 R' = (1,1)
 S' = (0,1) 
 The new cordinates for point q(1,0)