Answer:
9 units
Step-by-step explanation:
First of all, let us understand the meaning of dilation.
Dilation means to change the size of any image or line or a figure.
Dilation can be used to enlarge (dilation by a factor greater than 1) the original figure.
OR
Dilation can be used to make the image smaller (dilation by a factor lesser than 1) the original figure.
Here, we are given that an image with 4 points ABCD is dilated by a scale factor of [tex]\frac{1}{3}[/tex].
Its sides will be AB, BC, CD and DA.
Perimeter is equal to the sum of all the sides of a closed figure.
So, perimeter of ABCD = AB + BC + CD + DA = 27 units ...... (1)
Now, it is dilated by a scale factor of [tex]\frac{1}{3}[/tex].
So, all the sides will become smaller i.e.
A'B' = [tex]\frac{1}{3}[/tex] AB
B'C' = [tex]\frac{1}{3}[/tex] BC
C'D' = [tex]\frac{1}{3}[/tex] CD
D'A' = [tex]\frac{1}{3}[/tex] DA
Perimeter of A'B'C'D' = A'B' + B'C' + C'D' + D'A' = [tex]\frac{1}{3}[/tex]AB + [tex]\frac{1}{3}[/tex]BC + [tex]\frac{1}{3}[/tex]CD + [tex]\frac{1}{3}[/tex]DA
[tex]\frac{1}{3}[/tex] (AB + BC + CD + DA ) = [tex]\frac{1}{3} \times 27[/tex](By equation (1))
Perimeter of A'B'C'D' = 9 units
