Given a rectangle is transformed using the rule (x,y)→(-x,-y),what transformation occurred?Rotation or reflection.If Rotation name the direction and degrees and if reflection name the line.
I think it's Rotation 180 degrees.Is that correct?
correct ... rotation about the origin
No, the given transformation is actually a reflection. It reflects the rectangle across the origin (0,0), resulting in each point being transformed to its opposite (-x, -y).
No, it is not a rotation. The given rule (x,y) → (-x, -y) is actually a reflection. To understand this, let's delve into what each transformation means.
Rotation is a transformation that involves rotating an object around a point, known as the center of rotation, by a certain angle. In this case, the given rule does not involve any angle nor a center of rotation. Therefore, it cannot be a rotation.
Instead, the given rule (-x, -y) represents a reflection. A reflection is a transformation that "flips" an object over a line called the line of reflection. The rule (-x, -y) reflects the rectangle across the origin (0,0), flipping it horizontally and vertically.
So, the correct answer is reflection, and the line of reflection is the origin (0,0).