Question

1. describe the transformation that has occurred on the graph to the right. (pay attention to which is the pre-image & which is the image) the default direction of rotation: ____________

Explanation:

For the transformation description:

Step1: Identify Pre - Image and Image

The upper triangle (with vertices like \( Q \), \( R \), \( M \)) is the pre - image, and the lower triangle (with vertices \( Q' \), \( R' \), \( M' \)) is the image.

Step2: Analyze Vertical Shift

Looking at the \( y \) - coordinates of corresponding vertices. For example, if we take vertex \( R \) (pre - image) and \( R' \) (image), the \( y \) - coordinate of \( R \) is higher than that of \( R' \). By counting the grid units, we can see that the pre - image has been translated downwards. Let's assume the vertical distance between corresponding points (e.g., \( R \) and \( R' \)) is 8 units (by counting the grid squares). So the transformation is a vertical translation (shift) down by 8 units. The pre - image is the upper triangle, and the image is the lower triangle after moving down 8 units.

For the default direction of rotation:

In standard mathematical conventions, the default direction of rotation (when not specified otherwise) is counter - clockwise. This is a widely accepted convention in geometry, especially when dealing with rotations in the coordinate plane (e.g., when rotating around the origin or a point, the default is counter - clockwise unless stated as clockwise).

Answer:

s:

• Transformation: The pre - image (upper triangle) is translated vertically down by 8 units to get the image (lower triangle).
• Default direction of rotation: Counter - clockwise