When you have two shapes to compare on a coordinate plane, you can determine the scale factor, knowing that the transformation was a dilation. generate instructions you would give another student to determine the scale factor.

Assume that the initial coordinates are (x,y) and that the dilated coordinates are (x',y').

The dilation is therefore:
(x,y) > (x',y')

Now, let's assume that the dilation factor is k.
Therefore:
x' = kx
y' = ky

Based on the above, all the student has to do is get the initial coordinates and the final ones and then substitute in any of the above two equations to get the value of k.

Example:
Assume an original point at (2,4) is dilated to coordinates (4,8). Find the dilation factor.
Assume the dilation coefficient is k.
(x,y) are (2,4) and (x',y') are (4,8)
Therefore:
x' = kx > 4 = k*2 > k = 2
or:
y' = ky > 8 = k*4 > k = 2
Based on the above, the dilation coefficient would be 2.

Hope this helps :)