Question

Alexi transformed figure L such that its image is figure K after a 90degree counterclockwise rotation about the origin and a reflection over the y-axis.

On a coordinate plane, triangle K has points (negative 3, 1), (negative 1, 2), (negative 2, 5). Triangle L has points (2, negative 1), (1, negative 3), (5, negative 2).

Jonathan used figure L to perform the same transformation, but he reflected figure L over the y-axis before performing the 90degree counterclockwise rotation. Which best compares Alexi’s and Jonathan’s transformed figures?
The change in order will not affect the final image. Their transformed figures will be identical.
The change in order will result in the transformed images having vertices in the same location, but in a different orientation.
The change in order will result in the transformed image of figure L being transformed back onto figure L.
The change in order will result in the transformed image of figure L having a different location.

Answer 1

Answer: The change in order will result in the transformed image of figure L having a different location.

Quick check: take L point (2, −1).
- Alexi: rotate 90° CCW: (2, −1) → (1, 2). Then reflect over the y-axis: (1, 2) → (−1, 2).
- Jonathan: reflect first: (2, −1) → (−2, −1). Then rotate 90° CCW: (−2, −1) → (1, −2).

Those are different points, so the two orders produce images in different locations.