Question

Quadrilateral ABCD is transformed according to the rule (x, y) = (y; -x). Which is another way to state the transformation?

Answer 1

The given transformation rule (x, y) = (y, -x) is equivalent to a rotation of 90 degrees counterclockwise followed by a reflection across the x-axis.

Step-by-step explanation:

The transformation rule given in the question is (x, y) = (y, -x). To restate this transformation, we need to recognize what this rule does geometrically to a point in the Cartesian coordinate system.

Since the x-coordinate becomes the y-coordinate, and the y-coordinate becomes the negative of the x-coordinate, this transformation is equivalent to a rotation of 90 degrees counterclockwise followed by a reflection across the x-axis.

This two-step process can be visualized by considering a point and its transformation: Taking any point (x, y), rotate it 90 degrees counterclockwise, which would have normally landed at (-y, x), and then reflect this result across the x-axis to arrive at (y, -x), matching our original transformation rule.