Questions: Below is polygon KLMN. Complete the following transformations and give the new coordinates. a. Translation: 1 unit left and 3 units down b. Reflection: across the y-axis

Below is polygon KLMN. Complete the following transformations and give the new coordinates. a. Translation: 1 unit left and 3 units down b. Reflection: across the y-axis
Transcript text: Below is polygon KLMN. Complete the following transformations and give the new coordinates. a. Translation: 1 unit left and 3 units down b. Reflection: across the $y$-axis
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Solution

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Solution Steps

Step 1: Identify the original coordinates
  • \( K (3, -5) \)
  • \( L (2, 1) \)
  • \( M (-1, 2) \)
  • \( N (-3, -3) \)
Step 2: Apply the translation (1 unit left and 3 units down)
  • Translation rule: \( (x, y) \rightarrow (x - 1, y - 3) \)
  • New coordinates:
    • \( K' (3 - 1, -5 - 3) = (2, -8) \)
    • \( L' (2 - 1, 1 - 3) = (1, -2) \)
    • \( M' (-1 - 1, 2 - 3) = (-2, -1) \)
    • \( N' (-3 - 1, -3 - 3) = (-4, -6) \)
Step 3: Apply the reflection across the y-axis
  • Reflection rule: \( (x, y) \rightarrow (-x, y) \)
  • New coordinates:
    • \( K'' (-2, -8) \)
    • \( L'' (-1, -2) \)
    • \( M'' (2, -1) \)
    • \( N'' (4, -6) \)

Final Answer

  • After translation:
    • \( K' (2, -8) \)
    • \( L' (1, -2) \)
    • \( M' (-2, -1) \)
    • \( N' (-4, -6) \)
  • After reflection:
    • \( K'' (-2, -8) \)
    • \( L'' (-1, -2) \)
    • \( M'' (2, -1) \)
    • \( N'' (4, -6) \)
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