Short Answer 
The process for rotating a point 180 degrees around the origin involves transforming the coordinates from (x, y) to (-x, -y). For example, point L (2, 2) becomes L’ (-2, -2), and point N (1, 6) becomes N’ (-1, -6). The transformation rule is consistently applied to negate both the x and y values.
Step 1: Understand the Rotation Rule
The process of rotating a point 180 degrees around the origin changes its coordinates. Specifically, any point represented as (x, y) will transform to (-x, -y). This means that both the x and y values will be negated. This rotation effectively flips the point across both axes in the coordinate plane.
Step 2: Apply the Rule to Given Points
Now, let’s see how this rule applies to specific points. For instance, if we have a point L with coordinates (2, 2), applying the transformation yields:
- Coordinates of L’ = (-2, -2)
Similarly, with point N which has coordinates (1, 6):
- Coordinates of N’ = (-1, -6)
Step 3: Summarize the Results
From the transformations applied, we can draw key conclusions about the changes in coordinates. Note the following statements that are true:
- The transformation rule is (x, y) ‚ÄöUi (-x, -y).
- The coordinates of L’ are (-2, -2).
- The coordinates of N’ are (-1, -6).