Final answer:
In mathematics, the relationship between a pre-image and an image involves transformations like translation (moving horizontally or vertically) and rotation. Horizontal shifts occur to the right or left in the coordinate system, and vertical shifts occur upwards or downwards. A 90-degree counter clockwise rotation turns each point of the pre-image around the center of rotation to a new orientation.
Step-by-step explanation:
The relationship between the pre-image and image in transformations can involve shifting (translation), rotating, reflecting, or dilating. When an object on a coordinate plane is moved 6 units to the right, this is a horizontal shift to the right side of the coordinate system. If it is also moved 2 units down, that's a vertical move downward in the coordinate system. A description of the pre-image being moved 2 units up and 3 units left involves a vertical shift upwards and a horizontal move to the left side of the coordinate system. Conversely, if the pre-image is said to move 3 units to the left and 2 units up, it entails a horizontal move leftward and a vertical shift upward.
When discussing rotations, such as a transformation specifying that the pre-image was rotated 90 degrees counter clockwise, one might visualize this action like looking down on a merry-go-round turning counter clockwise. Each point on the pre-image moves along a curved path relative to the center of rotation, resulting in a new orientation of the image.