ABCD has a perimeter of 27 units and is dilated by a scale factor of 1/3. What is the perimeter of A¹B¹C¹D¹?

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 .

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 .

So, all the sides will become smaller i.e.

A'B' = AB

B'C' = BC

C'D' = CD

D'A' = DA

Perimeter of A'B'C'D' = A'B' + B'C' + C'D' + D'A' = AB + BC + CD + DA

(AB + BC + CD + DA ) = (By equation (1))

Perimeter of A'B'C'D' = 9 units

3

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