Math worksheet on transformations, focusing on identifying rotations of geometric shapes on coordinate planes.

To solve this problem, we need to identify which of the three shapes on the right is a rotation of the red shape on the left.

What is a rotation?
A rotation means turning a shape around a point (like spinning a wheel). The shape stays the same size and keeps its original orientation (it doesn't get flipped like a reflection or stretched like a dilation). It just points in a different direction.

Here is the step-by-step solution for each row:

Row 1: The Triangle
* Original Shape: A right-angled triangle with the vertical side on the left and the horizontal side on the bottom.
* Option 1 (Middle): This triangle is flipped upside down and backwards. This is a reflection, not a rotation.
* Option 2 (Right-middle): This triangle is much smaller than the original. This is a dilation (shrinking), not a rotation.
* Option 3 (Far Right): This triangle is turned so the long side is on the bottom and the point is at the top right. If you take the original triangle and turn it 90 degrees clockwise, it matches this shape perfectly.
* Answer: Circle the third image (the large triangle on the far right).

Row 2: The Rectangle
* Original Shape: A wide, horizontal rectangle.
* Option 1 (Middle-left): This is a very thin, tall rectangle. The proportions are wrong.
* Option 2 (Middle-right): This is a square. The original was a rectangle. The shape changed.
* Option 3 (Far Right): This is a tall, vertical rectangle. It has the same width and height as the original, just turned sideways. If you rotate the original rectangle 90 degrees, it becomes this vertical rectangle.
* Answer: Circle the fourth image (the vertical rectangle on the far right).

Row 3: The Trapezoid
* Original Shape: A trapezoid sitting flat on its long base.
* Option 1 (Middle-left): This shape looks like it was flipped over (reflected). Notice how the slanted sides are swapped compared to a simple turn.
* Option 2 (Middle-right): This shape is standing up on its short side. If you take the original flat trapezoid and turn it 90 degrees counter-clockwise (to the left), it stands up exactly like this one.
* Option 3 (Far Right): This shape is also standing up, but if you look closely at the angles, it is a mirror image of Option 2. Since Option 2 is the correct rotation, this one is incorrect.
* Answer: Circle the third image (the middle-right trapezoid standing on its side).

Row 4: The Triangle
* Original Shape: An isosceles triangle pointing upwards.
* Option 1 (Middle-left): This triangle is pointing to the left. If you take the original triangle and turn it 90 degrees counter-clockwise (to the left), it points exactly in this direction. The size and shape match perfectly.
* Option 2 (Middle-right): This triangle is huge. It is a dilation (enlargement).
* Option 3 (Far Right): This triangle is pointing downwards. While this *is* a rotation (180 degrees), usually in these problems, we look for the primary rotation options provided. However, looking at the layout, the first option (pointing left) is a standard 90-degree rotation. Let's re-evaluate. Actually, looking at the grid coordinates:
* Original Base: Width 8 units (from x=2 to x=10). Height 5 units (y=1 to y=6).
* Option 1: Base is vertical, length 5 units? No, let's look closer. The triangle in Option 1 has a vertical side of length 4 and horizontal of length 3? No, it looks like a scaled-down version or a different triangle. Let's look at Option 3.
* Option 3: Points down. Base width 8 units (x=2 to x=10). Height 5 units (y=-1 to y=-6). This is an exact match for a 180-degree rotation.
* Let's re-examine Option 1. The vertices seem to be roughly (-2,-1), (-5,-4), (-2,-7). Side lengths don't match the original (8, 5, 5).
* Let's re-examine Option 3. Vertices are (2,-1), (10,-1), (6,-6). This is an exact copy of the original triangle, just moved down and flipped. Wait, a 180-degree rotation around the origin would move (2,1) to (-2,-1). The image in Option 3 is at positive X values. This is a translation + rotation or just a rotation around a different point.
* Let's look at the "Rotation" definition again. Usually, it implies rotating around the origin or a vertex.
* Let's look at Row 1 again. The answer was clearly the one that preserved size and shape.
* Let's look at Row 4 again.
* Original: Base 8, Height 5.
* Image 2 (Middle Left): Looks smaller.
* Image 3 (Middle Right): Looks bigger.
* Image 4 (Far Right): Base 8, Height 5. It is pointing down. This is a 180-degree rotation.
* Therefore, the correct match is the one that preserves the dimensions.
* Answer: Circle the fourth image (the triangle on the far right pointing downwards).

Final Answer:
1. Row 1: Circle the 3rd image (the triangle on the far right).
2. Row 2: Circle the 4th image (the vertical rectangle on the far right).
3. Row 3: Circle the 3rd image (the trapezoid in the middle-right position).
4. Row 4: Circle the 4th image (the triangle on the far right).