To solve the problem of reflecting Figure $B$ across line $l$, let's analyze the image:

1. Identify the reflection line $l$: The given line $l$ passes through the origin and appears to have a slope of $-1$, so its equation is $y = -x$.

2. Reflection rules across $y = -x$: To reflect a point $(x, y)$ across $y = -x$, swap the coordinates and change their signs: $(x, y) \to (-y, -x).$

3. Vertices of Figure $B$: Extract the vertices of the polygon $B$. They seem to be:

   • $(5, 5)$,
   • $(7, 5)$,
   • $(7, 8)$,
   • $(5, 10)$.

4. Apply the reflection transformation: Reflect each vertex using the rule for $y = -x$:

   • $(5, 5) \to (-5, -5)$,
   • $(7, 5) \to (-5, -7)$,
   • $(7, 8) \to (-8, -7)$,
   • $(5, 10) \to (-10, -5)$.

5. Plot the reflected figure: The reflected polygon will have vertices at $(-5, -5)$, $(-5, -7)$, $(-8, -7)$, and $(-10, -5)$.

Would you like me to provide a visualization of the reflection or verify anything further?

Related Questions:

1. How do you derive the general reflection formula across a line?
2. Can you reflect figures across vertical or horizontal lines?
3. How does the slope of the line affect reflections geometrically?
4. What would happen if the reflection line was $y = x$ instead?
5. How do you calculate distances between points after a reflection?

Tip: To confirm the accuracy of reflections, check that the distance of each vertex from the line is equal on both sides.