Final answer:
The composition rule in mathematics is about combining functions, represented as f(g(x)). A coordinate rule for composition specifies how to combine two geometric transformations into one, like combining translation and rotation.
Step-by-step explanation:
The composition rule often refers to a rule in mathematics that concerns the combination of two functions. When we compose two functions, say f(x) and g(x), we're creating a new function where we first apply g to our input and then apply f to the result of g(x).
This is expressed as f(g(x)). For coordinate transformations, a coordinate rule for composition combines two transformations into one. Suppose we have a point (x, y) and want to apply two transformations: a translation by (a, b) followed by a rotation of 90 degrees around the origin.
First, we apply the translation, so (x, y) becomes (x+a, y+b). Then we rotate the result, which for a 90-degree rotation becomes (-(y+b), x+a). Hence, the coordinate rule for this composition would be from (x, y) to (-(y+b), x+a).