If point P (2,-8) is reflected across the line y = -2, what are the coordinates of its reflection image?
To find the reflection image of point P across the line y = -2, we first need to find the distance between point P and the line y = -2, and then move the same distance in the opposite direction.
The distance between point P and the line y = -2 is 8 units (from y = -8 to y = -2). To find the reflection image, we need to move 8 units in the opposite direction from y = -2.
Since the line of reflection is horizontal, the y-coordinate of the reflection image will stay the same, but the x-coordinate will change. Moving 8 units in the opposite direction from y = -2 means moving in the positive direction, so the new y-coordinate of the reflection image will be 2 units above y = -2, which is y = 2.
Therefore, the coordinates of the reflection image of point P across the line y = -2 is (2,2).