Final answer:
The rule for translating an object 2 units down and 3 units to the left is to subtract 3 from the x-coordinate and 2 from the y-coordinate of each point on the object. This translation shifts every point of the object left on the x-axis and downward on the y-axis without altering its shape or orientation.
Step-by-step explanation:
The rule for translating an object 2 units down and 3 units to the left is a mathematical instruction that shifts the position of every point of the object by the given amounts in each direction. For any point (x, y) on the object, the transformed coordinates (x', y') after the translation will be calculated as follows:
This means that if you have a point on the object at coordinates (5,5), translating the object according to the rule would shift that point to (2,3). The '2 units down' is visually represented on a graph as moving every point of the object two units in the negative y direction. Similarly, '3 units to the left' means moving every point of the object three units in the negative x direction. The translation does not change the shape or orientation of the object, merely its position.