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.