What combination of transformations is shown below? 1 3 rotation, then reflection translation, then rotation translation, then reflection rotation, then translation 2
The Correct Answer and Explanation is:
The correct answer is rotation, then reflection.
Explanation:
A combination of transformations means applying more than one transformation to a figure to map it onto its image. The common transformations include:
- Rotation: Turning a figure around a fixed point called the center of rotation by a certain angle.
- Reflection: Flipping a figure over a line, called the line of reflection, creating a mirror image.
- Translation: Sliding a figure from one place to another without rotating or flipping it.
In the scenario given, the correct sequence is rotation followed by reflection. Let me explain how this works:
Step 1: Rotation
- The figure is first rotated around a fixed point. This changes the orientation of the figure but keeps its size and shape the same. The position of the figure changes depending on the angle and direction of rotation, but the figure itself does not flip or reflect at this stage.
Step 2: Reflection
- After rotation, the figure is reflected over a specific line. Reflection produces a mirror image of the figure. The figure’s size and shape remain unchanged, but its orientation reverses across the line of reflection.
This sequence can often be identified by observing the final image:
- If the image has been rotated compared to the original, you know a rotation occurred.
- If the image is also flipped over a line (for instance, letters or shapes appear mirrored), then a reflection took place after the rotation.
This combination of rotation followed by reflection is a common transformation pattern in geometry, especially in problems dealing with symmetry, congruence, and mapping figures on a coordinate plane. It is important to apply the transformations in the correct order because transformations are not always commutative. That means doing reflection first and then rotation can result in a different final image compared to doing rotation first and then reflection.
