Question

what transformation is represented by the rule (x,y)→(-y,x)?

Answer 1

@Bobo-i-bo

Answer 2

Plot three points on a graph to form a triangle. The see what happens to the triangle when you apply the transformation. Do you get what i mean?

Answer 3

yes

Answer 4

i got reflection over the x-axis

Answer 5

Linearity means, "If you know how the basis vectors transform, you can transform any vector" so you can choose (1,0) and (0,1) as your basis vectors and see how those transform.

In symbols, linearity means you have some vector \(\vec v=x\hat i + y \hat j\) and your operator works like this:

\[A\vec v = x (A \hat i) + y (A \hat j)\]

You can see here that A only acts on the basis vectors.

@Devonhoward15 Are you sure it's a reflection? Is it possible that it only looks like a reflection? Try transforming the triangle again or try transforming a scalene triangle.

Answer 6

180 degree rotation?

Answer 7

@Kainui

Answer 8

Compare your problem with
(x, y) --> (x, -y)
This is not your problem.
In this case, every y coordinate becomes the opposite value, so this is actually a reflection over the x-axis. In your case, there is more going on, so it is not simply a reflection over the x-axis.