7. If point P (-2,1) is reflected across the line y = 2, what are the coordinates of its reflection image?

*
(4, -5)
(-2, 3)
(0, 1)
(1, 3)

1 answer

To find the reflection of point P \((-2,1)\) across the line \(y = 2\), we need to follow these steps:

1. Determine the vertical distance from point P to the line \(y = 2\).
2. Use that distance to find the reflection.

1. **Calculate the vertical distance:**

The y-coordinate of point P is 1. The line y = 2 is horizontal, so we find the distance between y-coordinates of P and the line.

Distance = \( |1 - 2| = 1 \)

2. **Find the reflection:**

The reflection will be the same distance from the line \(y = 2\) but in the opposite direction.

Since the original point P is 1 unit below the line \(y = 2\), its reflection will be 1 unit above the line \(y = 2\).

Reflected y-coordinate = \( 2 + 1 = 3 \)

The x-coordinate remains unchanged in a reflection across a horizontal line, so the x-coordinate of the reflected point is still \(-2\).

Therefore, the coordinates of the reflected point are:
\((-2, 3)\)

The correct answer is:
\((-2, 3)\)