L6.2 - Transformations as Functions
Learning Intentions and Success Criteria
- Describe (using words and other representations) transformations as functions that take points in the plane as inputs and give other points as outputs.
- Use coordinate transformation notation to take points in the plane as inputs and give other points as outputs.
2.1: Math Talk: Transforming a Point
- Translate A by the directed line segment from (0,0) to (0,2).
- Translate A by the directed line segment from (0,0) to (-4,0).
- Reflect A across the x-axis.
- Rotate A 180 degrees clockwise using the origin as a center.
2.2: Inputs and Outputs
1. For each point (x, y), find its image under the transformation (x + 12, y - 2). a. A = (-10, 5)
b. B = (-4, 9)
c. C = (-2, 6)
2. Next, create triangle ABC and its image on the grid. What transformation is (x, y) → (x + 12, y - 2)?
3. For each point (x, y) in the table, find (2x, 2y).
4. Next, create the original figure (the (x, y) column) and image (the (2x, 2y) column) in the above applet. What transformation is (x, y) → (2x, 2y)?
2.3: What Does it Do?
Here are some transformation rules. Apply each rule to quadrilateral ABCD and graph the resulting image. Then describe the transformation. 1. Label this transformation Q: (x, y) → (2x, y)
2. Label this transformation R: (x, y) → (x, -y)
3. Label this transformation S: (x, y) → (y, -x)
Lesson Synthesis: Transformations as Functions
Letters h and k represent numbers. Record ideas about what each rule represents.
Learning Intentions and Success Criteria
- Describe (using words and other representations) transformations as functions that take points in the plane as inputs and give other points as outputs.
- Use coordinate transformation notation to take points in the plane as inputs and give other points as outputs.
Cool-Down: Ready? Transform!
1. Transform triangle ABC using the rule (x, y) → (-x, y).
2. Describe the transformation precisely.