Question

Which sequence of transformations maps triangle ABC onto triangle DEF.

1. a reflection over the x-axis followed by a reflection over the y axis

2. a 180 rotation about the origin followed by a reflection over the line y=x

3. a 90 degree clockwise rotation about the origin followed by a reflection over the y-axis

4. a translation 8 units to the right and one units followed by a 90 degree counterclockwise rotation about the origin

20 point reward

Answer 1

D. a reflection over the x-axis and then a reflection over the y-axis

Explanation:

EDGE2020

Answer 2

1. a reflection over the x-axis followed by a reflection over the y axis

Explanation:

The sequence of corresponding vertices is CCW for both triangles, so an even number of reflections (or a rotation) is involved. (This eliminates choices 2 and 3.)

Segment AB is in the opposite direction of segment DE, so rotation by 90° cannot be involved. (This eliminates choice 4.)

Triangle DEF is apparently a rotation about the origin by 180° of triangle ABC. The equivalent is reflection across both axes. (Matches choice 1.)