Question

a triangle is rotated 90° about the origin. which rule describes the transformation?
(x, y) → (-x, -y)
(x, y) → (-y, x)
(x, y) → (-y, -x)
(x, y) → (y, -x)

Explanation:

Step1: Recall rotation rule

For a 90 - degree counter - clockwise rotation about the origin, the general rule is $(x,y)\to(-y,x)$.
For example, if we have a point $(2,3)$, after a 90 - degree counter - clockwise rotation about the origin, $x = 2$ and $y = 3$, and the new coordinates are $(-3,2)$.
This rule is derived from the properties of rotation in the coordinate plane and the relationships between the original and rotated coordinates.

Answer:

B. $(x,y)\to(-y,x)$