Answer:
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Cos(2 arctan(4/3)) = cos(2 arccos(3/5)) = cos^2(arccos(3/5)) - sin^2(arccos(3/5)) = cos^2(arccos(3/5)) - sin^2(arcsin(4/5)) = (3/5)^2 - (4/5)^2 = 9/25 - 16/25 = -7/25.
ANSWER
Scale factor is 1.25
The dilation is an enlargement.
EXPLANATION
Let the scale factor of the dilation be k, then

We divide both sides by 5 to get,

This implies that,

Since the scale factor is more than one, the dilation is an enlargement.