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.
To determine whether the transformation is a rotation or a reflection, we need to analyze the effects of the rule (x,y) → (-x,-y) on the rectangle.
In this rule, both the x-coordinate (horizontal direction) and the y-coordinate (vertical direction) of a point are negated. Let's consider the effects on a point in the rectangle:
1. Negating the x-coordinate (-x): This flips the point vertically across the y-axis. For example, if the original point is (2, 3), after negating the x-coordinate, it becomes (-2, 3).
2. Negating the y-coordinate (-y): This flips the point horizontally across the x-axis. For example, if the original point is (2, 3), after negating the y-coordinate, it becomes (2, -3).
Now, let's apply these effects on the rectangle:
- If we negate the x-coordinate of all the points in the rectangle, it will result in a reflection across the y-axis.
- If we negate the y-coordinate of all the points in the rectangle, it will result in a reflection across the x-axis.
Since the given rule involves negating both the x-coordinate and the y-coordinate of a point, it represents a combination of reflections across both the x-axis and the y-axis.
Therefore, the transformation that occurred is a reflection, specifically a reflection across both the x-axis and the y-axis.