To reflect a figure across a line we need to change it's points in such a way that the distance from the lines remains the same, but the sides are opposite. So the points A, B, C and D should still have the same distance from y=-2, but they must be positioned on the other side of that line.
We first need to calculate the distance that each point has from the line.
Point A:
The coordinates for the point A are (-2,-1) Since the line is y=-2, then point A is one unit above the line. It's new coordinate should be (-2,-3), because now it will be one unit below the line.
Point B:
The coordinates for the point B are (-1,3). Since the line is y=-2, then point B is 5 units above the line. It's new coordinate should be (-1, -7), because now it will be 5 units below the line.
Point C:
The coordinates for the point C are (3,2). Since the line is y=-2, then point C is 4 units above the line. It's new coordinates should be (3,-6), because now it will be 4 units below the line.
Point D:
The coordinates for the point D are (2,-1). Since the line is y=-2, then point D is one unit above the line. It's new coordinates should be (2,-3).
The new coordinates for the points are: A(-2,-3); B(-1,-7); C(3,-6) and D(2,-3).