The question in the image asks to "Reflect Triangle $ABC$ across line $\ell$" and label the corresponding points as $A'$, $B'$, and $C'$.

Steps to reflect Triangle $ABC$ across the line $\ell$:

1. Identify the coordinates of the vertices $A$, $B$, and $C$ on the grid.

   • $A$ is positioned at (5, 2)
   • $B$ is positioned at (8, 2)
   • $C$ is positioned at (7, 5)

2. Reflect each point across the vertical line $\ell$:

   • The reflection line $\ell$ is a vertical line that passes through $x = 6$.

3. Find the reflected points:

   • To reflect over a vertical line, for any point $(x, y)$, the reflected point is given by $(2k - x, y)$, where $k$ is the x-coordinate of the line of reflection, which in this case is 6.

   Using this formula:

   • For $A(5, 2)$, the reflection $A'$ will be at $(2(6) - 5, 2) = (7, 2)$.
   • For $B(8, 2)$, the reflection $B'$ will be at $(2(6) - 8, 2) = (4, 2)$.
   • For $C(7, 5)$, the reflection $C'$ will be at $(2(6) - 7, 5) = (5, 5)$.

4. Plot the points $A'$, $B'$, and $C'$ on the graph and draw the reflected triangle.

Would you like further assistance with plotting, or do you have any questions about this?

Here are five questions to expand your understanding:

1. How do you reflect a point across a horizontal line?
2. What is the formula for reflecting over a line like $y = x$?
3. How does the distance from the reflection line relate to the original and reflected points?
4. Can you explain why the y-coordinates remain unchanged in this reflection?
5. How would you rotate triangle $ABC$ 90° around the origin?

Tip: When reflecting across a line, the perpendicular distance from each point to the line remains the same after reflection!