Question

Determine whether each statement about the design from the rug is true.

Ashti is designing a rug that uses shapes to tell a
story, similar to what rug weavers in her culture
have done for generations. She uses a computer
program to dilate the shapes for the design of the
rug. One of Ashti's designs is shown below with
labels for figures 1 and 2 and points X, Y,and Z.
Select True or False for each statement.
The center of dilation for figures 1 and 2 is point Y.

Answer 1

I am really not sure

Answer 2

Each statement about the design from the rug should be completed as follows;

The center of dilation for figures 1 and 2 is point Y: False.

Figure 2 can be dilated by a scale factor of 3/2 to form figure 1: True.

Figure 1 can be dilated by a scale factor of 1/2 to form figure 2: False.

If figure 1 were dilated to form figure 2, figures 1 and 2 would have the same orientation: True.

In Mathematics and Euclidean Geometry, dilation is a type of transformation that is used for altering the dimensions of a geometric figure, but not its shape.

By critically observing the design, we can logically deduce that the center of dilation for figures 1 and 2 is point Z.

Note: Each interval on the set of axis represents 1 unit.

For the scale factor that was used to dilate figure 2 to figure 1, we have;

Scale factor = side length of image/side length of pre-image

Scale factor = 3/2

For the scale factor that was used to dilate figure 1 to figure 2, we have;

Scale factor = side length of image/side length of pre-image

Scale factor = 2/3

If figure 1 were dilated to form figure 2, figures 1 and 2 would have the same orientation: True.

In conclusion, dilation preserve the shape, orientaion, and angle size of a geometric figure.

Missing information:

The question is incomplete and the missing figure is shown in the attached picture.