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The coordinates of the vertices of the trapezoid are *W*(-9,3), *X*(-5, 3), Y(-2,-5), and *Z*(-9,-5). What are the coordinates of the image, trapezoid *W’X’Y’Z’*?

Let's work through the transformations step by step to find the coordinates of the image trapezoid \( W'X'Y'Z' \).

### Step 1: Reflect the trapezoid across the y-axis
We are reflecting the points across the y-axis. For each point \( (x, y) \), this means we change the sign of the \( x \)-coordinate.

The original coordinates of the trapezoid \( WXYZ \) are:
- \( W(-9, 3) \)
- \( X(-5, 3) \)
- \( Y(-2, -5) \)
- \( Z(-9, -5) \)

After reflecting across the y-axis, the new coordinates become:
- \( W' = (9, 3) \)
- \( X' = (5, 3) \)
- \( Y' = (2, -5) \)
- \( Z' = (9, -5) \)

### Step 2: Rotate the reflected image 90° clockwise about the origin
To rotate a point 90° clockwise about the origin, we transform the coordinates using the rule \( (x, y) \to (y, -x) \).

Applying this rule to each of the reflected points:
- \( W'(9, 3) \to (3, -9) \)
- \( X'(5, 3) \to (3, -5) \)
- \( Y'(2, -5) \to (-5, -2) \)
- \( Z'(9, -5) \to (-5, -9) \)

### Step 3: Translate the rotated image using the rule \( (x, y) \to (x+2, y-4) \)
Finally, we apply the translation rule \( (x, y) \to (x+2, y-4) \) to the rotated points.

- \( W'(3, -9) \to (3+2, -9-4) = (5, -13) \)
- \( X'(3, -5) \to (3+2, -5-4) = (5, -9) \)
- \( Y'(-5, -2) \to (-5+2, -2-4) = (-3, -6) \)
- \( Z'(-5, -9) \to (-5+2, -9-4) = (-3, -13) \)

### Final Coordinates of the image \( W'X'Y'Z' \):
- \( W' = (5, -13) \)
- \( X' = (5, -9) \)
- \( Y' = (-3, -6) \)
- \( Z' = (-3, -13) \)

Now you can fill in the blanks for \( W'X'Y'Z' \) based on these coordinates.

Do you want more details or have any questions? Here are 5 related questions:

1. What is the general rule for reflecting a point across the x-axis?
2. How does a 180° rotation differ from a 90° clockwise rotation?
3. What happens to a point when it is reflected over the origin?
4. How would the trapezoid look if rotated 90° counterclockwise instead?
5. What if we translated the figure using a different rule, like \( (x-2, y+4) \)?

**Tip:** When reflecting points, always be sure to change the appropriate coordinate (x or y) based on the axis of reflection.

The coordinates of the vertices of the trapezoid are W(-9,3), X(-5,3), Y(-2,-5), and Z(-9,-5). What are the coordinates of the image, trapezoid W'X'Y'Z'?

Solve a geometry problem involving the reflection, rotation, and translation of trapezoid WXYZ. Learn how to apply coordinate transformations to find the new vertices W', X', Y', and Z'. Suitable for students in Grades 8-10.

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