## Transformation: reflection over the line y=x

A. (x, y) (x 3, y + 5) (x 3, y + 5) (x 3, y + 5) (x 3, y + 5) (x 3, y + 5) (x 3, y This transformation is a congruence transformation that reflects a translation. The size and shape of the figure are maintained by translating all points 3 units to the left and 5 units up.
C. (x, y)Incorrect (x, -y). This transformation is a congruence transformation that reflects a representation around the x-axis. The figure’s size and form are retained, but all points on the figure are mirrored.
(-y, x)Incorrect. D. (x, y)Incorrect. This transformation is a congruence transformation that describes a 90° counterclockwise rotation around the origin. The figure’s size and form are retained despite the fact that all points on the figure are rotated.

## How to rotate a point 270 degrees counter clockwise

A fractal that looks like a fern (Barnsley’s fern) and has affine self-similarity. An affine transformation connects each of the fern’s leaves to the other leaves. By integrating reflection, rotation, scaling, and translation, the red leaf can be converted into the dark blue leaf as well as any of the light blue leaves.
An affine transformation, also known as an affinity (from the Latin affinis, “associated with”), is a geometric transformation in Euclidean geometry that preserves lines and parallelism (but not necessarily distances and angles).
An affine transformation is a function that maps an affine space onto itself while preserving both the dimension of any affine subspaces (that is, it sends points to points, lines to lines, planes to planes, and so on) and the ratios of the lengths of parallel line segments. As a consequence, after an affine transformation, sets of parallel affine subspaces remain parallel. An affine transformation does not always preserve angles between lines or distances between points, but it does preserve distance ratios between points on a straight line.

### Rotate 180 degrees around the origin

A rigid transformation (also known as an isometry) is a plane transformation that maintains length. “Rigid transformations” include reflections, translations, rotations, and variations of these three transformations.
A reflection over line m (notation rm ) is a transformation in which each point of the original figure (pre-image) has an image on the opposite side of the line that is the same distance from the reflection line as the original point. Since the image is the same size and shape as the pre-image, a reflection is called a rigid transformation or isometry.
The distances between the pre-image points and the image points differ (and are not necessarily equal) in this reflection that maps ABC to A’B’C’, but the segments representing these distances are parallel.
Orientation (lettering): The points of the pre-image are lettered clockwise A-B-C in this diagram, while the image is lettered counterclockwise A’-B’-C’. The transformation is known as a non-direct or opposite isometry when lettering changes direction in this way.

### Writing a translation rule

The first thing I found was MR’s, which said, “Translate ABC using vector AA.” I noticed she was mapping the triangle on the left side of the page onto the triangle on the right side of the page when I looked closer, but even if she had been mapping the triangle onto itself, she had come up with a surprisingly simple solution.
At this point, I decided that a class discussion would be helpful in limiting additional trivial solutions to this challenge. So far, we’ve discussed transformations that can, of course, map the figure into itself, such as rotating the image around one of its vertices 0 or 360, but which are also fairly basic and uninteresting.
Then I gave them some more time to work. The plan was for them to write a transformation or a series of transformations and then make their partner try it out, following their instructions to the letter. If the instructions didn’t work the first time, the partner assisted in revising them as required.
Several students speculated that the rectangle’s diagonals might be reflection points. Max was appointed as the Live Host, and he explained what happens when a rectangle is reflected about its diagonal.