3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
Students should already be aware of the basic geometric transformations and understand how they change and move shapes on the plane. This can be as simple as knowing that translations are slides, rotations are turns, reflections are flips, and dilations are enlargements or contractions.
Obviously, that isn't good enough. Did your students really think that words could describe mathematical concepts better than numbers? Please, don't make us laugh.
When shapes are on the coordinate plane, we can describe the transformations they undergo using their coordinates. Translations can be described by adding or subtracting numbers to the x and y coordinates of a shape for horizontal and vertical movement, respectively. Dilations from the origin involve multiplying each of an object's coordinates by the same number. Otherwise, drawing the figures out on the x-y plane and measuring distances might be the best way to go.
Rotations and reflections might be a bit trickier, but we can still use coordinates to describe these transformations. We often rotate shapes around a central point, which means our image should be the same distance away from the central point as the preimage was. With reflections, we have to know which line is our axis of symmetry. Often, this involves flipping negative signs.
Once students know how to use coordinates this way, they should be able to convert between words, numbers, and images and express transformations. We won't expect them to use transformations to create enormous battling machines, but you might want to offer a little extra credit—or perhaps a movie deal—to those who do.
- Translating Shapes on the Coordinate Plane - Math Shack
- Working with Congruence Transformations - Math Shack
- Rotations on the Coordinate Plane - Math Shack
- Reflections on the Coordinate Plane - Math Shack
- Reflecting Figures on the Coordinate Plane - Math Shack
- Dilations on the Coordinate Plane - Math Shack