Rectangle LMNP was dilated using the rule DP,3. Which statements are true? Check all that apply. The length of line segment M'N' is 18 units. The length of segment M'N' is 14 units. The dilation is a reduction. The dilation is an enlargement. The scale factor is 1/3. The scale factor is 3.

A dilation is a type of transformation that enlarges or reduces a figure .If the image is bigger than the original figure it is called Enlargement .If the image is smaller than the original figure it is called Dilation.

In the given figure Rectangle LMNP was dilated using the rule DP,3 to form the new figure L'M'N'P'. The sides of the image are enlarged by a scale factor 3.

The length of line segment M'N' is 6x3=18 units

Among all the given options the one which are true are:

The length of line segment M'N' is 18 units.

The dilation is an enlargement.

The scale factor is 3.

MrRoyal MrRoyal · Answer 2 · 2021-10-25T17:44:56+02:00

Transformation involves changing the size of a shape.

The true options are:

(a) The length of segment M'N' is 18 units
(d) The dilation is an enlargement.
(f) The scale factor is 3

From figure, we have:

[tex]\mathbf{LM =4}[/tex]

[tex]\mathbf{MN =6}[/tex]

[tex]\mathbf{L'M' =12}[/tex]

[tex]\mathbf{k =3}[/tex] --- scale factor

So, we have:

[tex]\mathbf{M'N' = k \times MN}[/tex]

[tex]\mathbf{M'N' = 3 \times 6}[/tex]

[tex]\mathbf{M'N' = 18}[/tex]

Because L'M'N'P' is bigger, then the dilation is an enlargement.

Hence, the true options are: (a), (d) and (f)