Final answer:
To find the reflection of point P=(-4,3) across the line y=1, the x-coordinate (-4) remains the same and the y-coordinate is reflected to 2 units below the line y=1, resulting in the reflected point (-4, -1).
Step-by-step explanation:
Given a point p=(-4,3), the question asks to find the reflection of point P across the line y = 1, which is denoted as Ry = 1 (P). To reflect point P across a horizontal line, the x-coordinate remains the same, while the y-coordinate changes based on its distance from the line of reflection.
To calculate the reflection, we keep the x-coordinate of P the same, which is -4. The y-coordinate changes by twice the distance between the original y-coordinate and the y = 1 line. In this case, the original y-coordinate is 3, and it is 2 units above the line y = 1 (since 3 - 1 = 2). So, we reflect point P to 2 units below the line y = 1, which would be at 1 - 2 = -1 for the y-coordinate.
Thus, the coordinates of the reflected point is (-4, -1).