Final answer:
A coordinate rule for the composition of transformations describes how to map a point from its original position to a new position by applying each transformation in sequence. For instance, the composition of a translation and a rotation is determined by first translating each point, followed by rotating the translated points.
Step-by-step explanation:
To answer the student’s question effectively, we need to understand the concept of coordinate rules in the context of compositions of transformations in geometry. A coordinate rule is a function that describes how to map a point from its original position to a new position in a coordinate system. Given that a student is asked to write a coordinate rule for compositions, they need to define how two separate transformations combine to form a single resultant transformation.
The question implies that exercises 9 and 10 previously provided specific transformations for which students must determine the resulting coordinate rule when these are composed. For example, if one transformation is a translation and another is a rotation, the coordinate rule for the composition would reflect the combined effect of both actions on any point in the plane. Generally, this requires applying the first transformation to the coordinates, and then applying the second transformation to the result of the first.
If the question included specific transformations, such as translating a point by 3 units up and 5 units to the right, followed by rotating 90 degrees counterclockwise about the origin, then the coordinate rule to describe this composition might be written as:
- Apply the translation: (x, y) → (x + 5, y + 3)
- Apply the rotation: (x', y') → (-y', x')
The composite rule would be: (x, y) → (-y + 3, x + 5). This rule shows how to carry out both transformations on any given point (x, y) in sequence.