To describe the translation of an image with the transformation [tex]\((x, y) \rightarrow (x+3, y-1)\)[/tex], we need to understand how each coordinate point [tex]\((x, y)\)[/tex] changes following the given rule.
Let's break this down step-by-step:
1. Original Coordinates: Consider any point on the image with coordinates [tex]\((x, y)\)[/tex].
2. Translation Definition: The transformation rule [tex]\((x, y) \rightarrow (x+3, y-1)\)[/tex] tells us how to obtain new coordinates from the original ones:
- The x-coordinate of each point increases by 3 units.
- The y-coordinate of each point decreases by 1 unit.
3. Effect on X-Coordinate: Increasing the x-coordinate by 3 units means shifting the point to the right by 3 units on the coordinate plane.
4. Effect on Y-Coordinate: Decreasing the y-coordinate by 1 unit means shifting the point down by 1 unit on the coordinate plane.
Combining these observations, the translation described by the transformation [tex]\((x, y) \rightarrow (x+3, y-1)\)[/tex] moves each point in the image 3 units to the right and 1 unit down.
Therefore, the correct description of this translation is:
A translation three units right and one unit down.
