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

Solution

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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