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.