Quadrilateral ABCD is transformed according to the rule (x, y) → (y, –x). Which is another way to state the transformation?
Another way to state the transformation is (x, y) → (-y, x).
The given transformation rule states that each point (x, y) of the original quadrilateral ABCD is transformed into a new point (y, -x).
To understand this transformation more intuitively, let's look at an example:
Suppose we have a point A(x, y) in the original quadrilateral ABCD. Applying the given transformation rule, we replace x with y and y with -x to obtain the transformed point A':
A'(y, -x)
By applying this rule to all the points of the quadrilateral ABCD, we obtain the corresponding points A', B', C', and D' in the transformed quadrilateral A'B'C'D'.
Now, let's determine another way to state this transformation.
The transformation (x, y) → (y, -x) can be referred to as a "90-degree clockwise rotation" or simply a "clockwise rotation by 90 degrees". This means that the original figure is rotated 90 degrees in a clockwise direction around the origin.
Pick a few points and see what happens to them.
I see a reflection in the line y = x, and then a reflection in the x-axis