# geometry

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What translation rule can be used to describe the result of the composition of (x, y) (x – 9, y – 2) and (x, y) (x + 1, y – 2)?

I am stuck can you please explain

• geometry -

The first rule sends (x, y) to (x - 9, y - 2). That is, it slides every point to the left nine units and down two units.

The second rule slides every point to the right 1 unit and down 2 units.

The composition is combining the two transformations. In this case, they are both translations (slides), so it doesn't really matter which order you do them in.

The first translation could be written in vector form as <-9, -2> and the second is <+1, -2>. To figure out the combined effect, just add the components.

<-9 + (+1), -2 + (-2)>

<-8, -4>

So a single slide left 8 and down 4 does the same thing as the two rules combined.

(x, y) --> (x - 8, y - 4)

would be a translation rule to use.

Note: Sometimes the order you do transformations matters. For example, translate then reflect might be different from reflect, then translate. But in the case of two translations, it doesn't really matter which order you do the slides. You could have done rule 2 first, then rule 1 second.

That's because

(x - 9 - 2, y - 2 + 1) is the same as

(x - 2 - 9, y + 1 - 2).

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