## 1-10 Multiple Transformations

**Objective:**to describe a sequence of transformations that maps one figure onto another.

**Standard**: 8.G.2

In this lesson, we will combine the previous three lessons, translations, reflections, and rotations into a sequence, or series, of transformations.

## Example 1

In this example, notice the original figure is in blue. It has no tic marks. It is labeled ABCD. The image is in red. Notice it has 2 tic marks. It is labeled A"B"C"D". This means it is the SECOND image and there had to have been a first image/transformation before it.

We must describe the sequence of transformations that maps ABCD onto A"B"C"D".

Notice the second image the points are reflected. This means a reflection had to be one of the transformations. Since it reflected "left to right" or vice versa, it was

From there, you can see the image translated down 2 spots, using the rule, (x, y-2).

The final answer to this would be

We must describe the sequence of transformations that maps ABCD onto A"B"C"D".

Notice the second image the points are reflected. This means a reflection had to be one of the transformations. Since it reflected "left to right" or vice versa, it was

**reflected across the Y-axis**. To continue, it will be helpful to draw this reflection.From there, you can see the image translated down 2 spots, using the rule, (x, y-2).

The final answer to this would be

**a reflection across the y-axis and a translation using the rule (x, y-2).**## Example 2

For this example, the blue trapezoid is the original figure. In order to map it onto its image, a sequence of transformations can be described.

Since it is turned on its side, a rotation MUST be one of the transformations.

From there, the figure was

Since it is turned on its side, a rotation MUST be one of the transformations.

**A 90 degree CW rotation would put the image standing the same way.**From there, the figure was

**t****ranslated using the rule (x+5, y-7)**to map it directly on top of the final image.## Example 3

For this example, follow the blue arrows. The initial figure is in Quadrant I. The sequence of transformations that will map the original figure to the final image is

**a reflection across the y-axis AND then a reflection across the x-axis.**

You try! Describe the sequence of transformations that maps the original figure onto the image.