Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates

What you'll learn

1. Apply the coordinate rules for translations, reflections (across the x-axis and y-axis), rotations (90 degrees, 180 degrees, 270 degrees about the origin), and dilations (centered at the origin) to compute the image of a given point or set of vertices
2. Describe the effect of each transformation on the coordinates of a figure using precise coordinate notation -- for example, "a reflection across the y-axis maps (x, y) to (-x, y)"
3. Classify a transformation as rigid (translation, reflection, rotation) or non-rigid (dilation) and explain how the coordinate rules reveal whether side lengths are preserved or changed
4. Determine the image of a two-dimensional figure (triangle, rectangle, or other polygon) under a single transformation by applying the coordinate rule to every vertex, then plotting the image on the coordinate plane
5. Compare the pre-image and image of a figure under dilation with the pre-image and image under a rigid motion, articulating that dilation changes the size but preserves the shape, while rigid motions preserve both

Prerequisites

• Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations