https://file.aiquickdraw.com/mathbot/file/1728053624760xy8ch2tq.jpg

The image shows a parallelogram \( ABCD \) on a coordinate grid that is rotated 90° counterclockwise about the origin, forming a new parallelogram \( A'B'C'D' \). The task is to find the **y-coordinate of vertex \( D' \)** after the 90° rotation.

### Steps to solve the problem:

1. **Identify the original coordinates of vertex \( D \)**:
   From the diagram, it appears that the coordinates of vertex \( D \) are \( (1, -4) \).

2. **Apply the 90° counterclockwise rotation formula**:
   When a point \( (x, y) \) is rotated 90° counterclockwise about the origin, the new coordinates \( (x', y') \) are given by the transformation:
   \[
   (x', y') = (-y, x)
   \]
   For vertex \( D \), which is \( (1, -4) \):
   \[
   (x', y') = (-(-4), 1) = (4, 1)
   \]

Thus, the new coordinates of vertex \( D' \) are \( (4, 1) \). Therefore, the **y-coordinate of vertex \( D' \)** is **1**.

Would you like more details on this? Let me know if you have any questions!

### Related Questions:
1. What are the new coordinates for the other vertices \( A' \), \( B' \), and \( C' \) after the rotation?
2. How does rotating by 180° affect the coordinates of a point on a grid?
3. What is the rule for rotating points 90° clockwise?
4. How can you determine the area of a parallelogram from its vertices?
5. How can you find the slope of the sides of the parallelogram from the coordinates?

### Tip:
When rotating points, remember that a counterclockwise rotation by 90° swaps the coordinates and changes the sign of the original y-coordinate!

What is the y-value of the coordinates for vertex D' after a 90° counterclockwise rotation of parallelogram ABCD about the origin?

Learn how to find the y-value of vertex D' after a 90° counterclockwise rotation of parallelogram ABCD on a coordinate grid. This problem covers key geometry concepts, including transformations and rotations. Suitable for Grade 8 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation