Note that the perimeter of any quadrilateral is the sum of its sides.
[tex]P=\sum ^n_{i\mathop=1}a_i[/tex]
So it is always proportional to the length of any side,
[tex]P\propto a_i[/tex]
Note that the dilation either stretches of compresses the sides.
For the factor 1/2, each side of the quadrilateral will get multiplied by 1/2, which simply means that the sides will get halved.
So the new perimeter is given by,
[tex]P^{\prime}=\sum ^n_{i=1}(\frac{1}{2}a_i)=\frac{1}{2}\sum ^n_{i=1}(a_i)=\frac{1}{2}P[/tex]
Thus, the perimeter will also get halved due to the dilation.
Therefore, option A is the correct choice.
