The reflection of a point across a line involves finding a corresponding point that resides on the opposite side of the line at an equal distance. In this case, we are reflecting the point (2, 4) across the line y = 1.
To find the reflected point:
- Determine the distance from the point to the line: The y-coordinate of the point (4) is 3 units above the line y = 1 because 4 – 1 = 3.
- Calculate the reflected point’s y-coordinate: Since the reflected point will be the same distance below the line, subtract the distance from the line’s y-coordinate. Thus, the y-coordinate of the reflected point will be:
y = 1 - 3 = -2. - Keep the x-coordinate the same: The x-coordinate of the point (2) remains unchanged when reflecting over a horizontal line. So, the x-coordinate of the reflected point will still be 2.
Combining these results, the coordinates of the reflected point are (2, -2).
Thus, the image of the point (2, 4) when reflected across the line y = 1 is (2, -2).