What is "which shows the image of δrst after the rotation (x?

Here's information about identifying the image of a shape after a rotation, presented in Markdown format with links:

Understanding Rotations and Image Identification

When dealing with the question "which shows the image of δrst after the rotation," you're essentially being asked to identify the new position and orientation of the shape δrst after it has been turned around a specific point (the center of rotation) by a certain angle. Here's a breakdown of key concepts:

• Center of Rotation: This is the point around which the shape is turned. The location of the center of rotation is crucial because the distance between any point on the original shape and the center of rotation remains the same after the rotation.

• Angle of Rotation: This specifies how many degrees the shape is rotated. Rotations are typically measured in degrees and are either clockwise or counterclockwise. Common rotation angles are 90°, 180°, and 270°.

• Direction of Rotation: A rotation can be either clockwise (turning in the same direction as the hands of a clock) or counterclockwise (turning in the opposite direction). The direction matters!

• Image: The "image" is the new shape after the transformation (in this case, the rotation). It's essentially a copy of the original shape, but in a different position and/or orientation.

How to Identify the Correct Image:

1. Visualize the Rotation: Imagine physically turning the shape δrst around the specified center by the given angle and in the correct direction.

2. Pay Attention to Orientation: Rotations change the orientation of the shape. A 90° clockwise rotation, for example, will make a vertical line horizontal (and vice versa).

3. Check Relative Positions: The relative positions of points within the shape remain the same. For example, if 'r' is above 's' in the original shape, it will still be "above" 's' in the rotated image (though "above" might be in a different direction relative to the page).

4. Use Coordinate Geometry (if applicable): If the shape is defined by coordinates on a graph, you can use rotation transformation rules to calculate the new coordinates of each point.

   • For a 90° counterclockwise rotation about the origin: (x, y) becomes (-y, x)
   • For a 90° clockwise rotation about the origin: (x, y) becomes (y, -x)
   • For a 180° rotation about the origin: (x, y) becomes (-x, -y)

5. Eliminate Incorrect Options: Look for options that clearly do not represent a rotation of the original shape. For example, if an option shows a reflection or a change in size, it's incorrect.

Key Concepts Recap:

• Transformations: Rotations are a type of geometric transformation.
• Congruence: Rotations preserve congruence (size and shape). The image is congruent to the original shape.