The transformation rule (x, y) -> (-x, -y) is a 180º rotation about the origin, flipping points across both axes simultaneously. Therefore , rotation of 180° about the origin is correct .
The transformation rule (x, y) -> (-x, -y) represents a reflection across the origin.
This operation involves flipping a point or an object over both the x-axis and the y-axis simultaneously.
It is akin to folding the coordinate plane along both axes, resulting in a symmetrical image with respect to the origin.
The rule for a reflection across the x-axis is (x, y) -> (x, -y).
This transformation is characterized by keeping the x-coordinate unchanged while negating the y-coordinate, effectively mirroring the points across the x-axis.
A rotation of 90º counterclockwise about the origin follows the rule (x, y) -> (-y, x).
This rotation swaps the x and y coordinates and negates the original y-coordinate, creating a rotated version of the point or object.
For a rotation of 180º about the origin, the rule is (x, y) -> (-x, -y).
This transformation results in a point or object being flipped halfway around the origin, effectively performing both a reflection across the x-axis and the y-axis simultaneously.
The rule for a reflection across the y-axis is (x, y) -> (-x, y).
This operation involves keeping the y-coordinate constant while negating the x-coordinate, leading to a mirror image across the y-axis.
Question
What transformation is represented by the rule (x, y)→(−x, −y) ?
reflection across the x-axis
rotation of 180° about the origin
rotation of 90° counterclockwise about the origin
reflection across the y-axis