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

an advantage of the standard deviation is that it increases as the dispersion of the data increases. e. the interquartile range is preferred when the data are not skewed or no have outliers. an advantage of the standard deviation is that it uses all the observations in its computation.