Question

7 maya performs three transformations on figure wxyz to show that figures wxyz and wxyz are similar. she dilates the figure by a scale factor of 2 with center of dilation at the origin, rotates the image 90° counterclockwise around the origin, and then reflects that image across the x - axis. does the order of transformations matter? explain.

Explanation:

Step1: Analyze dilation property

Dilation changes size proportionally, doesn't depend on order with rotation and reflection for similarity.

Step2: Analyze rotation - reflection relation

Rotation and reflection are rigid - motions. Changing their order can change orientation and position of the final image. For example, rotating first then reflecting and reflecting first then rotating can result in different final positions and orientations of the figure.

Step3: Consider overall effect

Since rotation and reflection are non - commutative operations (order matters between them), and dilation is independent in terms of similarity but its order with rotation and reflection can affect the final result in terms of position and orientation, the order of transformations matters.

Answer:

Yes, the order of transformations matters. Rotation and reflection are non - commutative operations and the order in which they are applied along with dilation can change the position and orientation of the final figure.