Question

A Single Transformation and a Sequence of Transformations
On a coordinate plane, a triangle has points (1, 1), (4, 1) and (3, 2).

Use the figure to complete the transformations.

1. Reflect the triangle across the y-axis.

2. Reflect the image across the x-axis.

The final image is the same as what single transformation?
a translation 2 units to the left and 2 units down
a reflection across the y-axis
a 180° rotation about the origin
a clockwise rotation 90° about the origin

Answer 1

Start: (1,1), (4,1), (3,2).

1) Reflect across the y-axis: (x,y) -> (−x,y)
→ (−1,1), (−4,1), (−3,2).

2) Reflect that image across the x-axis: (x,y) -> (x,−y)
→ (−1,−1), (−4,−1), (−3,−2).

This overall map is (x,y) -> (−x,−y), which is a 180° rotation about the origin. So the correct choice is: a 180° rotation about the origin.