Reflections worksheet with six coordinate geometry problems requiring students to reflect shapes across specified lines.

Let me solve each reflection problem step by step.

Problem 1: Reflection Across Line y = -x
The shape appears to be an L-shape in the third quadrant. Let me identify the vertices from the graph.
Looking at the grid, the shape seems to have vertices at approximately: (-3, -2), (-3, -4), (-2, -4), (-2, -3), (-1, -3), (-1, -2)

Wait, let me look more carefully. The shape is in the lower-left area. It looks like an L-shape with vertices:
- (-3, -2), (-3, -4), (-2, -4), (-2, -3), (-1, -3), (-1, -2)


Actually, I need to reconsider the coordinates more carefully. Looking at the image again, the L-shape has these points: (-3, -2), (-3, -4), (-2, -4), (-2, -3), (-1, -3), (-1, -2). To reflect across y = -x, I swap and negate the coordinates using (x, y) → (-y, -x), which gives me (2, 3), (4, 3), (4, 2), (3, 2), (3, 1), (2, 1).

For the second problem, I'm looking at a triangle in the second quadrant with vertices around (-3, 3), (-1, 4), and (0, 1). Reflecting across y = x means swapping the coordinates to get (3, -3), (4, -1), and (1, 0), which places the reflected triangle in the fourth quadrant.

Now for the third problem, I see an L-shape in the first quadrant near the line x = 1. The vertices appear to be at (1, 2), (1, 4), (2, 4), (2, 3), (3, 3), and (3, 2). To reflect across x = 1, I use the formula (x, y) → (2-x, y), which gives me the reflected points (1, 2), (1, 4), (0, 4), (0, 3), (-1, 3), and (-1, 2).

For the fourth problem, there's a triangle in the first quadrant with vertices at (0, 0), (0, 3), and (4, 0). Reflecting across the y-axis using (x, y) → (-x, y) gives me (0, 0), (0, 3), and (-4, 0), placing the reflected triangle in the second quadrant.

Now looking at the fifth problem, I see a parallelogram in the first quadrant with vertices at (1, 2), (3, 2), (4, 4), and (2, 4). To reflect across y = 2, I apply (x, y) → (x, 4-y), which transforms the vertices to (1, 2), (3, 2), (4, 0), and (2, 0).

For the sixth problem, there's an L-shape in the fourth quadrant with vertices at (2, -2), (2, -4), (3, -4), (3, -3), (4, -3), and (4, -2). Reflecting across the x-axis using (x, y) → (x, -y) gives me (2, 2), (2, 4), (3, 4), (3, 3), (4, 3), and (4, 2).

I should double-check my vertex readings from the images to make sure I have the right coordinates before finalizing these reflections.