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

Solution:

Given (x, y)→(-x, -y)

We know that the coordinate axes are divided into 4 quarters.

(x,y) lies in Q-1, (-x,y) lies in Q-2, (-x,-y) lies in Q-3 and (x,-y) lies in Q-4.

We can clearly, see that there is a reflection shift in both the x coordinate and the y coordinate

So, the point in Q-1 is shifted to a point in Q-3

Hence, the transformation is 180° about the origin.

What transformation is represented by the rule (x, y)→(-x, -y)?

Summary:

Transformation is represented by the rule (x, y)→(-x, -y) is 180° about the origin.