Worksheet on rotation transformations of shapes on a coordinate plane.

I will solve this problem by analyzing each rotation task one by one. Let's start with the first one.

Problem 1: Rotate Shape A 90° clockwise about the origin.

First, look closely:
- Shape A is a rectangle in the first quadrant.
- Its vertices are at (1,2), (3,2), (3,0), and (1,0).
- I need to rotate it 90° clockwise around the origin (0,0).

Next, find information:
The rule for rotating a point (x, y) 90° clockwise about the origin is (x, y) → (y, -x).

Then, review the findings:
Let me apply this rule to each vertex of Shape A:
- (1,2) → (2, -1)
- (3,2) → (2, -3)
- (3,0) → (0, -3)
- (1,0) → (0, -1)

So, the rotated shape will have vertices at (2,-1), (2,-3), (0,-3), and (0,-1). This forms a rectangle in the fourth quadrant.

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Problem 2: Rotate Shape B 180° about (0,1).

First, look closely:
- Shape B is a rectangle in the first quadrant.
- Its vertices appear to be at (1,1), (3,1), (3,4), and (1,4).
- I need to rotate it 180° around the point (0,1).

Next, find information:
The rule for rotating a point (x, y) 180° about a point (a, b) is (x, y) → (2a - x, 2b - y).

Then, review the findings:
Applying this rule with (a, b) = (0, 1):
- (1,1) → (2*0 - 1, 2*1 - 1) = (-1, 1)
- (3,1) → (2*0 - 3, 2*1 - 1) = (-3, 1)
- (3,4) → (2*0 - 3, 2*1 - 4) = (-3, -2)
- (1,4) → (2*0 - 1, 2*1 - 4) = (-1, -2)

So, the rotated shape will have vertices at (-1,1), (-3,1), (-3,-2), and (-1,-2). This forms a rectangle in the second and third quadrants.

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Problem 3: Rotate Shape [incomplete]

The text for Problem 3 is cut off. It says "Rotate Shape about (" but doesn't specify the angle or the point of rotation. Without this information, I cannot solve this problem.

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Problem 4: [Incomplete]

Problem 4 has no instructions written below the graph. The graph shows a line segment, but there's no text indicating what transformation to perform.

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Problem 5: [Incomplete]

Problem 5 shows a triangle labeled E, but there's no instruction on what rotation to perform.

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Problem 6: [Incomplete]

Problem 6 is also incomplete, with no instructions provided.

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Conclusion:

I can only solve Problems 1 and 2 completely based on the given information.

Solution for Problem 1:
The rotated shape has vertices at (2,-1), (2,-3), (0,-3), and (0,-1).

Solution for Problem 2:
The rotated shape has vertices at (-1,1), (-3,1), (-3,-2), and (-1,-2).

Problems 3, 4, 5, and 6 cannot be solved because the instructions are incomplete or missing.