What is the new position of point (1, 0) after reflection across the line y = -2?

To determine the new position of the point (1, 0) after reflecting it across the line y = -2, we first consider the original point's position relative to the line of reflection. The point (1, 0) is located above the line y = -2.

The y-coordinate of the original point is 0, while the line of reflection has a y-coordinate of -2. To find the distance from the point to the line, we subtract the y-coordinate of the line from that of the point:

0 - (-2) = 2.

Thus, the point is 2 units above the line. When reflected across the line, it will be moved an equal distance below the line. Therefore, we subtract this distance from -2:

-2 - 2 = -4.

This results in the new point being at (1, -4). This understanding shows that reflecting across a horizontal line like y = -2 involves moving vertically the same distance on the opposite side of the line. Thus, the new position of point (1, 0) after reflection across the line y = -2 is indeed (1, -4).