Question

To reflect a point across the line y = 2, we simply take the y-coordinate of the point and subtract it from 2?

Answer 1

Reflecting a point across the line y = 2 requires subtracting twice the distance from the y-coordinate to 2 and keeping the x-coordinate the same, resulting in a reflected point of (x, 4 - y).

Step-by-step explanation:

Reflecting a point across the line y = 2 is not as simple as subtracting the y-coordinate of the point from 2. To reflect a point (x, y) across the line y = 2, you actually need to consider how far the point's y-coordinate is from 2, and then subtract twice that distance from 2. The new y-coordinate (y') of the reflected point would be y' = 2 - (y - 2) = 4 - y. The x-coordinate will remain the same since the line y = 2 is horizontal, and reflecting a point across a horizontal line does not affect its x-coordinate. Therefore, the reflected point becomes (x, 4 - y).