Describe the sequence of transformations that occurred. Include specific details about the transformations, including the lines of reflection, the degree of rotation, the number of units translated, and/or the scale factor.

Answer 1

To describe a sequence of transformations, we can consider a geometric figure undergoing a series of changes. Here is an example of a sequence that includes reflections, rotations, translations, and dilations:

1. Reflection:

   • The first transformation is a reflection over a line. Let's say we reflect the figure across the x-axis. This means that for every point (x, y) in the original figure, the corresponding point in the reflected image will be (x, -y).

2. Rotation:

   • Next, we can rotate the reflected figure 90 degrees clockwise about the origin. In geometric terms, the rotation of 90 degrees clockwise means that a point (x, y) will be transformed to (y, -x).

3. Translation:

   • After rotation, we can translate the figure. For instance, if we translate the figure 3 units to the right and 2 units up, this means that for every point (x, y), the new position will become (x + 3, y + 2).

4. Dilation:

   • Finally, we can apply a dilation centered at the origin with a scale factor of 2. This means that every point (x, y) in the translated figure will be transformed into (2x, 2y), effectively increasing the size of the figure while maintaining its shape.

In summary, the transformations were:

1. Reflection across the x-axis.
2. Rotation 90 degrees clockwise about the origin.
3. Translation 3 units right and 2 units up.
4. Dilation with a scale factor of 2 centered at the origin.

This combination of transformations will result in a new figure that is transformed from the original in a specific manner.