Question

A path between 3 cities is drawn on a map, creating the outlined region shown in the graph below.

The path between 3 cities forms a triangle. City A is at (2, 2), City B is at (4, 8), and City C is at (8, 4).

Which sequence of transformations would result in mapping the region onto itself?

A
.

a rotation 90-degrees counterclockwise about the origin and then a rotation 270-degrees counterclockwise about the origin

B.

a rotation 180-degrees counterclockwise about the origin and then a rotation 270-degrees counterclockwise about the origin

C.

a rotation 90-degrees counterclockwise about the origin and then a rotation 180-degrees counterclockwise about the origin

D.

a reflection across the y-axis and then a reflection across the x-axis

Answer 1

Answer: A.

Reason: Rotations add. A 90° CCW followed by 270° CCW is a 360° rotation, i.e. the identity map, which leaves the triangle unchanged. The other sequences give nonidentity rotations or a 180° rotation and do not map the triangle onto itself.