Question

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

Answer 1

9 units

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
`(1)/(3)`.

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
`(1)/(3)`.

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

A'B' =
`(1)/(3)` AB

B'C' =
`(1)/(3)` BC

C'D' =
`(1)/(3)` CD

D'A' =
`(1)/(3)` DA

Perimeter of A'B'C'D' = A'B' + B'C' + C'D' + D'A' =
`(1)/(3)`AB +
`(1)/(3)`BC +
`(1)/(3)`CD +
`(1)/(3)`DA

`(1)/(3)` (AB + BC + CD + DA ) =
`(1)/(3) * 27`(By equation (1))

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