The correct coordinates of the image point are (2, 4), so the answer is option D.
How to find the coordinates of the image
To find the coordinates of the image when the point (2, -4) is reflected across the line y = -1, determine the new y-coordinate.
The line y = -1 serves as the reflection line or the axis of symmetry. When reflecting a point across a line, the y-coordinate is negated if the point is above the line and remains the same if the point is below the line.
In this case, the point (2, -4) is below the line y = -1, so the y-coordinate remains the same.
Therefore, the image point will have coordinates (2, -(-4)) = (2, 4).
Comparing the options provided:
A. (5, 4) - Incorrect
B. (4, 2) - Incorrect
C. (2, 2) - Incorrect
D. (2, 4) - Correct
The correct coordinates of the image point are (2, 4), so the answer is option D.