If point P (-2,1) is reflected across the line y = 2, what are the coordinates of its reflection image?
*
(4, -5)
(3, -2)
(0, 1)
(1, 3)
The coordinates of the reflection image can be found by reflecting point P across the line y = 2.
Since the line y = 2 is a horizontal line, the reflection will result in a point whose y-coordinate is obtained by subtracting the difference between point P's y-coordinate and the line y = 2 from the line's equation.
In this particular case, the line y = 2 is 1 unit above point P's y-coordinate. When reflected across the line, we would get a point whose y-coordinate is 1 unit below the line y = 2. Thus, the y-coordinate of the reflection image would be 1 - 1 = 0.
To find the x-coordinate, we need to determine the horizontal distance between point P and the line y = 2, which is 1 unit. When reflected across the line, the x-coordinate of the reflection image would be the same distance in the opposite direction. Therefore, the x-coordinate of the reflection image would be -2 - 1 = -3.
Therefore, the coordinates of the reflection image are (-3, 0).
None of the multiple choice options match this.