Question

The pentagon ABCDE is dilated to the image A'B'C'D'E' with the center of the dilation at the origin.
Select all true statements

The scale factor of the dilation is 1/4
The line EA is parallel to the E’A’ because EA passes through the center of the dilation
Since the line C’D’ falls on the line CD, the scale factor is. It applied on the line CD
The scale factor of the dilation is 1/2
The line CD is not parallel to the line C’D’ because CD passes through the center of the dilation

Answer 1

Now I’m no genius but I‘m pretty sure the answers are “c” and “d”

Ya’ll have a good day or night, whichever one!

Answer 2

The true statement for the Pentagon in the given graph is

The scale factor of the dilation is 1/2 with the center at the origin(0,0).  

Dilation:  

Dilation implies resize of any object.

• It may increase or decrease the object by a particular value.

• The particular value is called the scale factor.

Properties of Dilation of figure:

• Parallel lines in the dilated figure remain the same as in the original figure.

• The dilation of any figure does not vary from each angle of the figure.

• The midpoints of the dilated figure remain the same as that of the original figure.

True statement:

The scale factor of the dilation of the pentagon is 1/2.

Reason:

• The pentagon with vertices A(0.5,4.5), B(2,3), C(1,0), D(-2,0), E(-3,3) when multiplied by 1/2 we get

• The vertices of the dilated pentagon as A'(0.25,2.25), B'(1,1.5), C'(0.5,0), D'(-1,0), E(-1.5,1.5).

• When we plot the points A'B'C'D'E' in the graph, obtain the dilated pentagon with a center at the origin.

Wrong statement with Reasons:

• The scale factor of the dilation is not 1/4 because when we multiply the vertices of pentagon ABCDE by 1/4 we are not getting the dilated points as in the graph.

• The line EA is parallel to E'A' but,

        1. The line EA does not passes through the center of the dilation

            at origin(0,0), which can be clearly seen from the given graph.

       2. For two lines to be parallel it is not necessary for one of the

            lines to pass through the origin.

• The line C'D' is parallel to CD as we should see the figure in a 3-dimensional way and it also follows the properties of dilation of a figure.

Hence the scale factor of the given pentagon is 1/2.

To learn more about the Dilation of polygons:

https://brainly.com/question/3020085?referrer=searchResults

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