Math worksheet featuring six transformation problems on coordinate grids, including reflections, rotations, and translations.

Let me work through each transformation problem step by step.

Problem 1: Reflection Across the x-axis
Looking at the shape, I need to identify its vertices and reflect them across the x-axis. The rule for reflection across the x-axis is (x, y) → (x, -y).

The original shape appears to be a stepped/polygon shape in the second quadrant. Let me identify the vertices from the grid:
- Looking at the shape, it appears to have vertices around (-4, 2), (-3, 2), (-3, 1), (-2, 1), (-2, 0), (-1, 0), (-1, -1)...

Wait, let me look more carefully. The shape is in the upper-left area. It looks like an L or stepped shape with vertices approximately at:
(-4, 2), (-3, 2), (-3, 1), (-2, 1), (-2, 0), (-1, 0), (-1, -1)...

Actually, looking again at the grid, the shape seems to be bounded between x = -5 to x = -1 and y = 0 to y = 2 roughly. Let me try to read the vertices more carefully.

The shape appears to have these vertices (going around):
(-5, 2), (-3, 2), (-3, 1), (-2, 1), (-2, 0), (-1, 0), (-1, -1)...

Hmm, this is getting complex. Let me just apply the reflection rule: (x, y) → (x, -y). Every point's y-coordinate gets negated.

Problem 2: Rotation 90° clockwise about the origin
Rule: (x, y) → (y, -x)

Problem 3: Reflection Across the line y = -1
The triangle has vertices that I need to identify, then reflect across y = -1.
Rule for reflection across y = k: (x, y) → (x, 2k - y)
So for y = -1: (x, y) → (x, -2 - y)

The triangle appears to have vertices at approximately (1, -1), (3, -1), (2, -3)... wait let me look again.

Looking at the triangle in problem 3, it appears to be in the lower right area with vertices around:
(1, -1), (3, -1), (2, -3) - this would be an upside-down triangle

Reflecting across y = -1:
- (1, -1) → (1, -2-(-1)) = (1, -1) [stays same, on the line]
- (3, -1) → (3, -1) [stays same]
- (2, -3) → (2, -2-(-3)) = (2, 1)

Problem 4: Translation 2 left and 3 down
Rule: (x, y) → (x-2, y-3)

The triangle appears to have vertices at approximately (1, 4), (3, 4), (2, 2).
After translation:
- (1, 4) → (-1, 1)
- (3, 4) → (1, 1)
- (2, 2) → (0, -1)

Problem 5: Translation 5 down
Rule: (x, y) → (x, y-5)

The shape appears to be in the upper right with vertices around (1, 4), (3, 4), (3, 2), (2, 2), (2, 1), (1, 1).
After translation 5 down:
- (1, 4) → (1, -1)
- (3, 4) → (3, -1)
- (3, 2) → (3, -3)
- (2, 2) → (2, -3)
- (2, 1) → (2, -4)
- (1, 1) → (1, -4)

Problem 6: Rotation 90° counterclockwise about the origin
Rule: (x, y) → (-y, x)

The trapezoid/shape appears to have vertices at approximately (-4, 2), (-1, 2), (-2, 0), (-3, 0).
After rotation 90° CCW:
- (-4, 2) → (-2, -4)
- (-1, 2) → (-2, -1)
- (-2, 0) → (0, -2)
- (-3, 0) → (0, -3)

Since all options are false, I just need to provide the Final Answer with the transformed coordinates for each problem.

Let me reconsider the shapes more carefully by looking at the image description.

For Problem 1, the shape looks like a stepped polygon. Let me try to identify vertices:
It appears to go from around (-5, 2) to (-3, 2) to (-3, 1) to (-2, 1) to (-2, 0) to (-1, 0) to (-1, -1)...

Actually, I think the shape might be simpler. Let me assume it's a polygon with clear integer coordinates.

Given the complexity of reading exact coordinates from the image, let me provide the transformation rules and describe what happens to each shape.

Actually, since the user wants me to solve the problems, I should provide the final transformed positions. Let me be more careful.

For a worksheet like this, the student needs to draw the transformed shapes. Since I can't draw, I'll describe the new vertex positions.

Let me finalize my answers based on reasonable coordinate readings:

Problem 1: Reflection across x-axis: (x,y) → (x,-y)
Original vertices (approximate): (-5,2), (-3,2), (-3,1), (-2,1), (-2,0), (-1,0), (-1,-1)...
Reflected: (-5,-2), (-3,-2), (-3,-1), (-2,-1), (-2,0), (-1,0), (-1,1)...

Problem 2: Rotation 90° CW about origin: (x,y) → (y,-x)

Problem 3: Reflection across y=-1: (x,y) → (x, -2-y)

Problem 4: Translation 2 left, 3 down: (x,y) → (x-2, y-3)

Problem 5: Translation 5 down: (x,y) → (x, y-5)

Problem 6: Rotation 90° CCW about origin: (x,y) → (-y, x)

Since I can't precisely determine all vertices from the image, I'll provide the transformation rules and key vertex transformations as the final answer.