# 3 Rigid Motions for Congruence: Translations, Reflections, and Rotations y₁ -6- 5- -4 ·3· N 1 -6 -5 -4 -3 -2 -1 0 -1+ --2 -3- --4- --5- -6 1 2 3 4 5 1. Show me each of these on the grid by drawing the 6 transformations of the "L". 2. Write the (x, y) rule 6 X that goes with each transformation in the given box like this: (x,y) →→ _____ (
# 3 Rigid Motions for Congruence: Translations, Reflections, and Rotations y₁ -6- 5- -4 ·3· N 1 -6 -5 -4 -3 -2 -1 0 -1+ --2 -3- --4- --5- -6 1 2 3 4 5 1. Show me each of these on the grid by drawing the 6 transformations of the "L". 2. Write the (x, y) rule 6 X that goes with each transformation in the given box like this: (x,y) →→ _____ (
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**#3 Rigid Motions for Congruence: Translations, Reflections, and Rotations**
The image depicts a Cartesian coordinate grid with an "L" shaped figure positioned in the first quadrant.
### Instructions:
1. **Transformations on the Grid:** Show each of the six transformations of the "L" shape on the grid. The transformations will involve translations (moving the shape), reflections (flipping the shape), and rotations (turning the shape).
2. **Writing (x, y) Rules:** For each transformation, write the rule that describes the change in coordinates in the format:
\( (x, y) \rightarrow ( \_\_\_, \_\_\_ ) \)
### Diagram Explanation:
- The grid spans from -6 to 6 on both the x-axis and y-axis, providing a range for plotting the transformations.
- The initial position of the "L" is at coordinates ranging from (3, 1) to (4, 3) in the first quadrant.
- The task involves observing how these coordinates will change with each transformation described.
Note: Students are expected to fill in the coordinate changes for each transformation and demonstrate the result on the grid.
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