Final answer:
Upon reflecting the coordinates of polygon MAST across the line x = -3, none of the provided options accurately represent the new coordinates of M', A', S', and T'. The correct reflected coordinates would be M'(-3, -1), A'(-3, 2), S'(-5, 3), T'(-7, 1), suggesting a potential error in the question or provided options.
Step-by-step explanation:
The student asks which of the given options represents the coordinates of polygon MAST after a reflection across the line x = -3. To find the reflected coordinates, recall that a reflection across a vertical line changes the x-coordinate of a point, while the y-coordinate remains the same. If a point (x, y) is reflected across a vertical line x = k, the new x-coordinate is x' = 2k - x. In this case, k=-3, so the formula for the new x-coordinate is x' = 2(-3) - x = -6 - x.
- For point M(-3, -1), x' = -6 - (-3) = -3, so M'(-3, -1).
- For point A(-3, 2), x' = -6 - (-3) = -3, so A'(-3, 2).
- For point S(-1, 3), x' = -6 - (-1) = -5, so S'(-5, 3).
- For point T(1, 1), x' = -6 - (1) = -7, so T'(-7, 1).
None of the options given by the student match these results. It seems there might be a mistake in the question or the options provided.