Final answer:
The rotation rule (x, y) → (y, -x) swaps the x-coordinate with the y-coordinate and negates the new x-coordinate, resulting in a rotated triangle.
Step-by-step explanation:
The rule (x, y) → (y, -x) represents a rotation of a triangle in the coordinate plane. This rule swaps the x-coordinate with the y-coordinate and negates the new x-coordinate. For example, if we have a triangle with vertices A(1, 2), B(3, 4), and C(5, 6), applying the rule would give us A'(2, -1), B'(4, -3), and C'(6, -5).
The rotation rule (x, y) → (y, -x) signifies a 90-degree counterclockwise rotation of a point on a coordinate plane, which if applied to a triangle, rotates the entire triangle by the same angle while maintaining its properties.
The rotation rule (x, y) → (y, -x) describes a 90-degree rotation of a point around the origin in the counterclockwise direction on the coordinate plane. For example, if we have a vector or a point (x, y) on a coordinate system, after applying this rule, the new position of the point would be (y, -x). This means that if the point was part of the vertices of a triangle, the entire triangle would undergo a rotation of 90 degrees counterclockwise. When we think of a triangle, we must envision a three-sided figure lying on a plane with three angles adding up to 180 degrees. The rotation would maintain this definition, merely altering the orientation of the triangle.