TRANSFORMATIONS : ROTATE,REFLECT, TRANSLATE? worksheet | Live ... - Free Printable

To solve the problem, we need to match each transformation description with the correct image. Let's analyze each transformation step by step.

1. Rotation, 90° anticlockwise about the centre origin

- Description: When an object is rotated 90° anticlockwise about the origin, each point \((x, y)\) of the object moves to \((-y, x)\).
- Image Analysis: Look for an image where the shape has been rotated 90° counterclockwise around the origin.
- Match: The top-left image shows a triangle that has been rotated 90° counterclockwise about the origin.

2. Translation \(\begin{pmatrix} 2 \\ 4 \end{pmatrix}\)

- Description: Translation means moving the object without rotating or flipping it. Here, each point \((x, y)\) moves to \((x+2, y+4)\).
- Image Analysis: Look for an image where the entire shape has been shifted 2 units to the right and 4 units up.
- Match: The bottom-left image shows a triangle that has been translated 2 units to the right and 4 units up.

3. Translation \(\begin{pmatrix} 3 \\ 3 \end{pmatrix}\)

- Description: Each point \((x, y)\) moves to \((x+3, y+3)\).
- Image Analysis: Look for an image where the entire shape has been shifted 3 units to the right and 3 units up.
- Match: The middle-left image shows a rectangle that has been translated 3 units to the right and 3 units up.

4. Reflection in the line x-axis

- Description: Reflecting over the x-axis means that each point \((x, y)\) moves to \((x, -y)\). The shape is flipped horizontally.
- Image Analysis: Look for an image where the shape is mirrored across the x-axis.
- Match: The middle-right image shows a shape that is reflected across the x-axis.

5. Reflection in the line y-axis

- Description: Reflecting over the y-axis means that each point \((x, y)\) moves to \((-x, y)\). The shape is flipped vertically.
- Image Analysis: Look for an image where the shape is mirrored across the y-axis.
- Match: The top-right image shows a shape that is reflected across the y-axis.

6. Rotation, 180° about the centre origin

- Description: Rotating 180° about the origin means that each point \((x, y)\) moves to \((-x, -y)\). The shape is flipped both horizontally and vertically.
- Image Analysis: Look for an image where the shape has been rotated 180° around the origin.
- Match: The bottom-right image shows a shape that has been rotated 180° about the origin.

Final Matches:

1. Rotation, 90° anticlockwise about the centre origin → Top-left image
2. Translation \(\begin{pmatrix} 2 \\ 4 \end{pmatrix}\) → Bottom-left image
3. Translation \(\begin{pmatrix} 3 \\ 3 \end{pmatrix}\) → Middle-left image
4. Reflection in the line x-axis → Middle-right image
5. Reflection in the line y-axis → Top-right image
6. Rotation, 180° about the centre origin → Bottom-right image

Answer:

\[
\boxed{
\begin{array}{ll}
\text{Top-left} & \text{Rotation, 90° anticlockwise about the centre origin} \\
\text{Bottom-left} & \text{Translation } \begin{pmatrix} 2 \\ 4 \end{pmatrix} \\
\text{Middle-left} & \text{Translation } \begin{pmatrix} 3 \\ 3 \end{pmatrix} \\
\text{Middle-right} & \text{Reflection in the line x-axis} \\
\text{Top-right} & \text{Reflection in the line y-axis} \\
\text{Bottom-right} & \text{Rotation, 180° about the centre origin} \\
\end{array}
}
\]