Final answer:
After reflecting the given points across the horizontal line y = -3, the coordinates of the reflected points are S'(-5, -10), R'(-2, -10), and both Q and P remain unchanged as Q'(-2, -3) and P'(-5, -3) because they lie on the line of reflection.
Step-by-step explanation:
When reflecting points across a line, the perpendicular distance from each point to the line will be the same for its reflection on the other side of the line. In the case of reflecting across the line y = -3, we need to visualize each point being 'flipped' over this horizontal line. If a point is a units above y = -3, its reflection will be a units below y = -3, and vice versa.
Let's reflect the points S(-5, 4), R(-2, 4), Q(-2, -3), and P(-5, -3) across the line y = -3.
- S'(-5, -10): The original point S is 7 units above the line y = -3, so the reflected point will be 7 units below, making it -3 - 7 = -10.
- R'(-2, -10): Similar to point S, R is 7 units above y = -3, so the reflected point will also be -3 - 7 = -10.
- Q'(-2, -3): Point Q lies on the line y = -3, so it will reflect onto itself.
- P'(-5, -3): Point P, like Q, lies on the line y = -3, so it too will reflect onto itself.
The coordinates of the vertices after a reflection across the line y = -3 for points S, R, Q, and P will be S'(-5, -10), R'(-2, -10), Q'(-2, -3), and P'(-5, -3) respectively.