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

The transformation rule (x,y) -> (-x,-y) is a

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Rotation of 180° about the origin.

Step-by-step explanation:

Given :  (x, y)→(−x, −y).

To find : What transformation is represented by the rule.

Solution : We have given that (x, y)→(−x, −y).

By the Rotation  rule of 180° about origin is  (x, y) → (−x, −y).

Coordinates of x change in to  -x  and coordinates of y change in to -y .

Example : is f(x) = ( 2 ,3) if we rotate it 180° about origin then f(x) = (-2,-3).

Therefore, rotation of 180° about the origin.