To solve this problem, we need to reflect the given points $L$, $M$, $K$, and $N$ over the line $y = -x$. Here's a step-by-step explanation:

Step 1: Identify the original coordinates

Let's find the original coordinates of each vertex:

• $L = (2, 9)$
• $M = (5, 9)$
• $K = (2, 6)$
• $N = (5, 6)$

Step 2: Reflect the points over the line $y = -x$

When reflecting a point over the line $y = -x$, the transformation rule is to swap the x and y coordinates and then change their signs. That is, a point $(a, b)$ reflects to $(-b, -a)$.

Applying this rule to each point:

• For $L = (2, 9)$, the reflected point is $L' = (-9, -2)$
• For $M = (5, 9)$, the reflected point is $M' = (-9, -5)$
• For $K = (2, 6)$, the reflected point is $K' = (-6, -2)$
• For $N = (5, 6)$, the reflected point is $N' = (-6, -5)$

Step 3: The reflected coordinates

The vertices after reflection over the line $y = -x$ are:

• $L' = (-9, -2)$
• $M' = (-9, -5)$
• $K' = (-6, -2)$
• $N' = (-6, -5)$

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. What is the general rule for reflecting a point over the line $y = x$?
2. How would you reflect a figure over the x-axis?
3. What happens to the coordinates when a point is reflected over the y-axis?
4. How do you determine the line of reflection between two points?
5. How would you describe the reflection of a figure over any arbitrary line, not just $y = -x$?

Tip: Always remember that reflecting over a line involves swapping coordinates and changing their signs as per the transformation rules associated with that line.