The question asks for the coordinates of the reflection of point $A$ across the line $y = 2$. Let's break this down:

1. The given point $A$ has coordinates $(2, -3)$.
2. The line of reflection is $y = 2$, which is horizontal.

Steps to Reflect:

To reflect a point across a horizontal line, you need to calculate the vertical distance from the point to the line and then place the reflection at the same distance on the opposite side.

• The vertical distance from point $A(2, -3)$ to the line $y = 2$ is: $|2 - (-3)| = 5$

• So, the reflection will be 5 units above the line $y = 2$. This places the new point at: $y = 2 + 5 = 7$

Thus, the coordinates of the reflection are $(2, 7)$.

Answer:

The reflected coordinates of point $A$ across the line $y = 2$ are $(2, 7)$.

Do you need more details on the reflection process or have any other questions?

Here are 5 related questions to explore further:

1. How would you reflect a point across a vertical line like $x = 1$?
2. What are the coordinates of a point reflected over the origin?
3. How would the reflection change if the line of reflection were $y = -2$?
4. Can you describe the reflection of a point across an arbitrary line $y = mx + c$?
5. How would you compute the reflection of multiple points across the same line?

Tip: For any reflection, always calculate the distance between the point and the line of reflection and then mirror that distance on the other side!