Let's solve this reflection problem step by step.

You are asked to reflect the quadrilateral $ABCD$ across the line $y = x$. The rule for reflecting a point $(x, y)$ over the line $y = x$ is to switch the coordinates, meaning the new point will be $(y, x)$.

Part A: Coordinates of $A'B'C'D'$

We need to identify the original coordinates of the points $A$, $B$, $C$, and $D$ from the graph, and then apply the reflection rule.

• Point $A$: The coordinates of $A$ appear to be $(-10, 0)$.

  • Reflecting over $y = x$, the new coordinates will be $A' = (0, -10)$.

• Point $B$: The coordinates of $B$ are $(-5, 5)$.

  • Reflecting over $y = x$, the new coordinates will be $B' = (5, -5)$.

• Point $C$: The coordinates of $C$ are $(5, 5)$.

  • Reflecting over $y = x$, the new coordinates will be $C' = (5, 5)$ (which stays the same).

• Point $D$: The coordinates of $D$ are $(0, -5)$.

  • Reflecting over $y = x$, the new coordinates will be $D' = (-5, 0)$.

Part B: Drawing the Reflection

To complete the task, you would plot the reflected points $A'$, $B'$, $C'$, and $D'$ on the graph.

Summary of Reflected Coordinates

• $A' = (0, -10)$
• $B' = (5, -5)$
• $C' = (5, 5)$
• $D' = (-5, 0)$

Would you like further details on any part of this reflection process? Let me know if you have questions!

Here are 5 related questions to expand your understanding:

1. How do you reflect a point across the line $y = -x$?
2. What is the general rule for reflecting points across the x-axis and y-axis?
3. How do the properties of a quadrilateral change under reflection?
4. Can reflection change the size of a shape? Why or why not?
5. How would the coordinates change if the reflection was across the y-axis instead?

Tip: Remember, reflecting a point over the line $y = x$ always switches its coordinates!