https://file.aiquickdraw.com/mathbot/file/1729478317593gxhvk0sa.jpg

To solve the given problem of rotating the figure DEFG 90° clockwise and then reflecting it over the y-axis, let's break it down step by step.

### Step 1: Coordinates of the vertices
From the image, the current coordinates of the vertices of the quadrilateral DEFG are approximately:
- \( D(-3, 2) \)
- \( E(-1, 2) \)
- \( F(-1, -4) \)
- \( G(-4, -3) \)

### Step 2: Rotation 90° clockwise
The rule for rotating a point 90° clockwise about the origin is:
\[
(x, y) \rightarrow (y, -x)
\]
Apply this transformation to each vertex:

- \( D(-3, 2) \rightarrow (2, 3) \)
- \( E(-1, 2) \rightarrow (2, 1) \)
- \( F(-1, -4) \rightarrow (-4, 1) \)
- \( G(-4, -3) \rightarrow (-3, 4) \)

After the 90° clockwise rotation, the new coordinates of the vertices are:
- \( D'(2, 3) \)
- \( E'(2, 1) \)
- \( F'(-4, 1) \)
- \( G'(-3, 4) \)

### Step 3: Reflection over the y-axis
The rule for reflecting a point over the y-axis is:
\[
(x, y) \rightarrow (-x, y)
\]
Now apply this transformation to each of the rotated points:

- \( D'(2, 3) \rightarrow (-2, 3) \)
- \( E'(2, 1) \rightarrow (-2, 1) \)
- \( F'(-4, 1) \rightarrow (4, 1) \)
- \( G'(-3, 4) \rightarrow (3, 4) \)

### Final coordinates after both transformations:
- \( D''(-2, 3) \)
- \( E''(-2, 1) \)
- \( F''(4, 1) \)
- \( G''(3, 4) \)

This is the final position of the quadrilateral after rotating it 90° clockwise and reflecting it over the y-axis.

Would you like more details, or do you have any questions about the process? 

Here are 5 related questions to further your understanding:
1. What is the rule for rotating a point 180° clockwise about the origin?
2. How would the figure change if we rotated it 90° counterclockwise instead?
3. What is the effect of reflecting the figure over the x-axis instead of the y-axis?
4. How do the coordinates change when reflecting over both axes sequentially?
5. How does the area of the figure change with these transformations?

**Tip**: When performing transformations, always apply rotations first, followed by reflections, to ensure correct positioning.

Rotate DEFG 90° clockwise then reflect over the y-axis.

Learn how to rotate the quadrilateral DEFG 90° clockwise and reflect it over the y-axis. This problem demonstrates essential geometry concepts such as transformations and coordinate geometry. Suitable for students in Grades 7-9.

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