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)