The reflection of the point (6, -3) on the line y = 2 is:

The correct answer is Option (2) → (6, 7)

To find the reflection of the point $(6, -3)$ across the line $y = 2$, we can follow these geometric steps:

1. Identify the Type of Reflection

The line $y = 2$ is a horizontal line. When you reflect a point across a horizontal line:

• The $x$-coordinate remains exactly the same.
• The $y$-coordinate changes based on its distance from the line.

2. Calculate the Vertical Distance

The original point is at $y = -3$. The line of reflection is at $y = 2$.

• Distance from the point to the line $= |2 - (-3)| = 5$ units.

3. Determine the Reflected $y$-coordinate

Since the original point is 5 units below the line $(y=2)$, the reflected point must be 5 units above the line.

• New $y$-coordinate $= 2 + 5 = 7$.

4. Combine the Coordinates

• The $x$-coordinate stays $6$.
• The new $y$-coordinate is $7$.
• Reflected point: $(6, 7)$.

Conclusion

The reflection of the point $(6, -3)$ on the line $y = 2$ is $(6, 7)$.