Name 3-1 Reteach to Build Understanding Reflections 1. Tell whether each transformation is a rigid motion or is not a rigid motion This is because the size and shape do This is because not change. the size changes 2. Example: The graph shows the reflection of quadrilateral ABCD across line m. The reflection is written R ABCD) – (A’B’CD). Esteban said RABO – (ABC), where the equation of line nis x4 is the rule for the reflection. What was his error? 3. Which is the line of reflection for each pair of figures? MacBook Air
The correct answer and explanation is:
3-1 Reteach to Build Understanding: Reflections
1. Rigid Motion or Not?
A rigid motion is a transformation that preserves the size and shape of a figure. Reflections, translations, and rotations are examples of rigid motions because they do not alter the dimensions of the figure.
- Rigid Motion: A reflection is a rigid motion because it flips a figure over a line without changing its size or shape.
- Not a Rigid Motion: A dilation is not a rigid motion because it changes the size of the figure, making it either larger or smaller.
2. Identifying the Error in the Reflection Rule
Esteban made an error in identifying the equation of the reflection line. His notation RABO → (ABC) is incorrect. The correct notation is:
[
R_m(ABCD) = A’B’C’D’
]
where line m is the line of reflection. If the equation of line m is x = 4, this means every point in quadrilateral ABCD is reflected across the vertical line at x = 4.
Esteban’s mistake: He wrote RABO → (ABC) instead of including all points D and D’. Also, his notation suggests a direct correspondence, but reflection involves flipping each point across the given line.
3. Identifying the Line of Reflection
To determine the line of reflection, follow these steps:
- Identify corresponding points in the original and reflected figure.
- Find the perpendicular bisector of any pair of corresponding points.
- The equation of this bisector is the line of reflection.
For example:
- If the reflection moves a shape across the x-axis, the line of reflection is y = 0.
- If a shape is reflected across the y-axis, the line of reflection is x = 0.
- If it is reflected across a diagonal, the line could be y = x or y = -x, depending on the orientation.
I will now generate an image illustrating the reflection of quadrilateral ABCD across a line.
Here is an image illustrating the reflection of quadrilateral ABCD across the vertical line ( x = 4 ). This visual representation helps in understanding how each point flips symmetrically over the given line of reflection. Let me know if you need any modifications or further explanations!
