Final answer:
To reflect triangle ABC across the line y=2, find the images of each vertex by measuring the perpendicular distance from the line y=2 and plotting points the same distance on the opposite side. The reflected triangle A'B'C' will have vertices A'(3,6), B'(-5,1), and C'(5,9). Sketch these on a graph with the mirror line to visualize the transformation.
Step-by-step explanation:
To reflect the triangle ABC with vertices A(3,-2), B(-5,3), and C(5,-5) across the line y=2, we must find the images of each vertex after reflection. The reflection of a point across a line is equidistant from the line and on the opposite side. To accomplish this, we can measure the perpendicular distance of each point from the line y=2 and duplicate this distance on the other side of the line.
For vertex A(3,-2), the perpendicular distance to the line y=2 is 4 units (since -2 is 4 units below 2 on the y-axis). Therefore, the image of A after reflection, A', will be 4 units above y=2, at the point (3, 2 + 4) = (3, 6).
For vertex B(-5,3), B is 1 unit above y=2. Thus, its image B' will be at (-5, 2 - 1) = (-5, 1).
For vertex C(5,-5), C is 7 units below y=2, so its image C' will be at (5, 2 + 7) = (5, 9).
The reflected triangle A'B'C' has vertices at A'(3,6), B'(-5,1), and C'(5,9). To visualize this, sketch the original triangle on a graph, draw the reflection line y=2, and plot the new vertices according to the calculated positions. Connect the new vertices to form the reflected triangle.
Note: The mirror line y=2 is the horizontal line through the point (0,2) and extends infinitely in both the positive and negative directions on the x-axis.