The problem involves plotting a trapezoid with vertices $W(7, 3)$, $X(4, 3)$, $Y(1, 9)$, and $Z(6, 5)$, and then performing some transformations.

Part (a):

You're asked to reflect the trapezoid using the transformation $(x \rightarrow -x, y \rightarrow y)$, and determine where $Y'$ (the image of point $Y$) is located after the reflection.

In the transformation, the $x$-coordinate changes its sign, while the $y$-coordinate stays the same. Let's apply the transformation to point $Y(1, 9)$:

• The new $x$-coordinate of $Y'$ becomes $-1$ (because $x \rightarrow -x$).
• The $y$-coordinate remains the same, so it stays at $9$.

Thus, after the reflection, $Y'$ will be located at $(-1, 9)$.

Part (b):

You need to name a sequence of at least two rigid transformations that will take $W'X'Y'Z'$ back to $WXYZ$.

To map $W'X'Y'Z'$ back to $WXYZ$, we can use the following transformations:

1. Reflection: Reflect $W'X'Y'Z'$ back across the y-axis (which negates the effect of the first transformation). This will turn $W'$, $X'$, $Y'$, and $Z'$ into the original points $W$, $X$, $Y$, and $Z$.
2. Translation: After the reflection, the figure might be displaced, so we would translate it back to the correct position. For instance, we can translate by $(6, 0)$ to adjust the horizontal shift that resulted from the reflection.

Would you like further details or assistance with plotting?