Describe a sequence of transformations that exhibits the similarity between the pair of figures shown.

The figure shows two rectangles DEFG and D'E'F'G'. The coordinates of the vertices DEFG are (-6, 1), (-6, 8), (0, 8), and (0, 1). The coordinates of D'E'F'G' are (-1.5,-0.25), (-1.5, -2), (0,-2), and (0,-0.25).

Please help

ugh this oobleck person is the most irritating person on this site. jump of the golden gate bridge and do a backflip while you're at it.

Well, it seems like our two rectangles are having quite a transformation party! Here's how they're getting similar:

1. Translation: Our first move is a translation since the rectangles seem to have shifted their positions. Rectangle DEFG decided to move -4.5 units to the right and -1.25 units downwards. Maybe it was trying to find better lighting?

2. Dilation: Next up, we have a dilation. Both rectangles seem to have changed their sizes. Rectangle DEFG decided to shrink itself. It got 1/4 times smaller in both width and height. Maybe it didn't want to take up too much space anymore?

3. Reflection: Lastly, it seems like our rectangles decided to take a glance in the mirror. Both rectangles ended up flipping upside down, reflecting around the x-axis. Maybe they wanted to see things from a different perspective?

So, if you want to exhibit the similarity between these two figures, just remember: Translation, Dilation, and Reflection. They're the life of the transformation party!

To show the similarity between the two rectangles DEFG and D'E'F'G', we will perform a sequence of transformations.

Step 1: Translation
We can perform a translation to move rectangle DEFG to the origin. We will move it so that the point D (-6, 1) coincides with the origin (0, 0). To achieve this, we add 6 to the x-coordinate and subtract 1 from the y-coordinate of each vertex of DEFG:
D: (-6+6, 1-1) = (0, 0)
E: (-6+6, 8-1) = (0, 7)
F: (0+6, 8-1) = (6, 7)
G: (0+6, 1-1) = (6, 0)

Now the translated rectangle DEFG' is at the origin, and its new vertices are (0, 0), (0, 7), (6, 7), and (6, 0).

Step 2: Dilation
Next, we will perform a dilation to change the size of the rectangle while keeping the shape intact. By comparing the corresponding sides of DEFG and D'E'F'G', we can determine that the scale factor is 0.25. We multiply each coordinate by 0.25:
D': (0 * 0.25, 0 * 0.25) = (0, 0)
E': (0 * 0.25, 7 * 0.25) = (0, 1.75)
F': (6 * 0.25, 7 * 0.25) = (1.5, 1.75)
G': (6 * 0.25, 0 * 0.25) = (1.5, 0)

Now the transformed rectangle D'E'F'G' is at the origin, and its new vertices are (0, 0), (0, 1.75), (1.5, 1.75), and (1.5, 0).

Step 3: Translation
Finally, we can perform a translation to move the transformed rectangle D'E'F'G' to its final position. To achieve this, we add 1.5 to the x-coordinate and add 0.25 to the y-coordinate of each vertex of D'E'F'G':
D': (0+1.5, 0+0.25) = (1.5, 0.25)
E': (0+1.5, 1.75+0.25) = (1.5, 2)
F': (1.5+1.5, 1.75+0.25) = (3, 2)
G': (1.5+1.5, 0+0.25) = (3, 0.25)

Now the final transformed rectangle D'E'F'G' is at its new position with vertices (1.5, 0.25), (1.5, 2), (3, 2), and (3, 0.25).

By performing the translation, dilation, and translation in sequence, we have shown the similarity between the two rectangles DEFG and D'E'F'G'.

To show the similarity between the two figures, we need to identify a sequence of transformations that can transform one figure into the other while preserving their shape.

1. Translation: The given figures have been translated horizontally by 4.5 units (from -6 to -1.5) and vertically by -1.25 units (from 1 to -0.25). Translate figure DEFG by 4.5 units to the right and 1.25 units down to match the position of figure D'E'F'G'.

2. Scaling: The given figures have been scaled equally in the x and y directions. To find the scale factor, we can compare the differences between the corresponding x and y coordinates of the vertices between the two figures.

For example, in the x direction, the width of DEFG is 6 (0 - (-6)), and the width of D'E'F'G' is 1.5 (0 - (-1.5)). So, the scale factor for the x direction is 1.5/6 = 0.25.

Similarly, in the y direction, the height of DEFG is 7 (8 - 1), and the height of D'E'F'G' is 1.75 (-0.25 - (-2)). So, the scale factor for the y direction is 1.75/7 = 0.25.

Now, apply the scaling factor to the translated figure DEFG. Multiply each x-coordinate by 0.25 and each y-coordinate by 0.25 to get the vertices of the scaled figure.

3. Reflection: If you compare the orientation of DEFG and D'E'F'G', you will notice that they are mirror images of each other. To reflect the scaled figure, reflect it across either the x-axis or the y-axis.

In this case, let's reflect the scaled figure across the x-axis. Negate the y-coordinates of all the vertices of the scaled figure.

The resulting figure is the transformed version of DEFG that is similar to D'E'F'G'.

To summarize the sequence of transformations:
1. Translate figure DEFG by 4.5 units to the right and 1.25 units down.
2. Scale the translated figure by a factor of 0.25 in both the x and y directions.
3. Reflect the scaled figure across the x-axis by negating the y-coordinates of its vertices.

Following these transformations will visually show the similarity between the original figure DEFG and the transformed figure D'E'F'G'.

clearly the size has been shrunk by a factor of 4

and it has been shifted, by how much?

Draw the diagram, and you can see that no rotation or reflection has occurred