https://file.aiquickdraw.com/mathbot/file/1725984748454e64zmpzc.jpg

To graph the image of the parallelogram \( ABCD \) after a translation of 5 units to the left and 2 units down, we need to adjust the coordinates of each vertex by these amounts.

1. **Translation rule**:  
   - Move each point left by 5 units: Subtract 5 from the x-coordinate.
   - Move each point down by 2 units: Subtract 2 from the y-coordinate.

Let’s apply this transformation to each vertex.

- Original coordinates of point **A**:  
  \( A(x_A, y_A) = (1, 4) \)  
  After translation:  
  \( A'(x_A - 5, y_A - 2) = (1 - 5, 4 - 2) = (-4, 2) \)

- Original coordinates of point **B**:  
  \( B(x_B, y_B) = (4, 4) \)  
  After translation:  
  \( B'(x_B - 5, y_B - 2) = (4 - 5, 4 - 2) = (-1, 2) \)

- Original coordinates of point **C**:  
  \( C(x_C, y_C) = (3, 1) \)  
  After translation:  
  \( C'(x_C - 5, y_C - 2) = (3 - 5, 1 - 2) = (-2, -1) \)

- Original coordinates of point **D**:  
  \( D(x_D, y_D) = (0, 1) \)  
  After translation:  
  \( D'(x_D - 5, y_D - 2) = (0 - 5, 1 - 2) = (-5, -1) \)

So, the new vertices of the translated parallelogram are:
- \( A'(-4, 2) \)
- \( B'(-1, 2)

Graph the image of the parallelogram ABCD after a translation of 5 units to the left and 2 units down.

Learn how to graph the image of a parallelogram ABCD after translating it 5 units to the left and 2 units down. This problem covers coordinate geometry concepts and the application of translation transformations. Suitable for Grade 8 students.

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