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The problem involves rotating parallelogram \( ABCD \) 90° counterclockwise about the origin, resulting in parallelogram \( A'B'C'D' \), and you're asked to find the y-coordinate of vertex \( D' \).

Let’s determine the y-coordinate step by step:

1. **Locate the coordinates of the original vertices:**
   - From the graph, the approximate coordinates of the vertices of parallelogram \( ABCD \) are:
     - \( A(1, -2) \)
     - \( B(3, -2) \)
     - \( C(4, -4) \)
     - \( D(2, -4) \)

2. **Apply a 90° counterclockwise rotation formula:**
   The rotation formula for a point \((x, y)\) rotated 90° counterclockwise about the origin is:
   \[
   (x', y') = (-y, x)
   \]

3. **Apply the formula to vertex \( D(2, -4) \):**
   - \( x' = -(-4) = 4 \)
   - \( y' = 2 \)

Thus, the coordinates of \( D' \) are \( (4, 2) \).

Therefore, the y-coordinate of vertex \( D' \) is \( \boxed{2} \).

Would you like more details or have any other questions? 



Parallelogram ABCD, shown on the coordinate grid, is rotated 90° counterclockwise about the origin, creating parallelogram A'B'C'D'. What is the y-value of the coordinates for vertex D'?

This geometry problem asks to find the y-coordinate of vertex D' after rotating parallelogram ABCD 90° counterclockwise about the origin. Using the rotation formula, learn how to calculate the transformed coordinates step-by-step.

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