Composing rotations about different points

[fk378]

Homework Statement

Suppose T is a rotation by 30 degrees about the point 2, and S is a rotation by 45 degrees about the point 4. What is T composed with S? Can you describe this transformation geometrically?

Homework Equations

none

The Attempt at a Solution

I know T composed with S means S is the first transformation we want to do, and T is second. But I'm not sure how we can rotate about the point 4, and then rotate about the point 2.

 

[tiny-tim]

Hi fk378!

Hold your hand out, and put in on a table … that's point 2.

Now rotate your whole body (keeping your arm stiff) 30º about point 2.

Let your feet now be at point 4.

Rotate your whole body (keeping your arm stiff) 45º about point 4.

What's the result? ​