https://file.aiquickdraw.com/mathbot/file/1729792900008ms5ql5cq.jpg

To solve this, we will apply a 90° counterclockwise rotation around the origin to each vertex of square \( EFGH \). A 90° counterclockwise rotation in the coordinate plane can be performed using the transformation rule:

\[
(x, y) \rightarrow (-y, x)
\]

Let's apply this rule to each vertex:

1. **Point E**: \( (3, 2) \)
   - After rotation: \( (-2, 3) \)

2. **Point F**: \( (6, 2) \)
   - After rotation: \( (-2, 6) \)

3. **Point G**: \( (6, 5) \)
   - After rotation: \( (-5, 6) \)

4. **Point H**: \( (3, 5) \)
   - After rotation: \( (-5, 3) \)

The new coordinates of the rotated square are:
- \( E' (-2, 3) \)
- \( F' (-2, 6) \)
- \( G' (-5, 6) \)
- \( H' (-5, 3) \)

These points form the image of square \( EFGH \) after a 90° counterclockwise rotation about the origin.

Would you like further details on graphing these points, or do you have any other questions?

### Related Questions:
1. What is the rule for a 180° rotation about the origin?
2. How would the transformation differ with a 90° clockwise rotation?
3. Can you explain the general formula for rotating any point by an arbitrary angle?
4. What happens when rotating points around a different center (not the origin)?
5. How do rotations affect the size and shape of geometric figures?

### Tip:
To easily visualize rotations, remember that each 90° rotation swaps and negates the coordinates systematically!

Graph the image of square EFGH after a rotation 90° counterclockwise around the origin.

Learn how to perform a 90° counterclockwise rotation of square EFGH on the coordinate plane. The solution involves applying the transformation rule (x, y) → (-y, x) to each vertex. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation