Question

(x, y)→(-y, x)

Explanation:

Since the problem is about a transformation of coordinates \((x, y) \to (-y, x)\), we can analyze this transformation in the context of Geometry (a subfield of Mathematics).

Step 1: Recall the rotation transformation formula

In coordinate geometry, a rotation of a point \((x, y)\) about the origin by \(90^\circ\) counter - clockwise is given by the transformation \((x,y)\to(-y,x)\), and a rotation of \(270^\circ\) clockwise (which is equivalent to a \(90^\circ\) counter - clockwise rotation) also has the transformation \((x,y)\to(-y,x)\).

Step 2: Identify the type of transformation

Given the transformation \((x, y)\to(-y, x)\), by comparing with the standard rotation transformation formulas, we can conclude that this transformation represents a rotation of the point \((x,y)\) about the origin. Specifically, it is a \(90^\circ\) counter - clockwise rotation about the origin (or a \(270^\circ\) clockwise rotation about the origin).

Answer:

The transformation \((x, y)\to(-y, x)\) represents a \(90^\circ\) counter - clockwise (or \(270^\circ\) clockwise) rotation about the origin.