Question

Polygons ABCD and A′B′C′D′ are shown on the following coordinate grid: What set of transformations is performed on ABCD to form A′B′C′D′? A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A polygonABCD is shown with vertex A on ordered pair 2, negative 2, vertex B on ordered pair 4, negative 2, vertex C on ordered pair 1, negative 3 and vertex D on ordered pair 5, negative 3. A polygonA prime B prime C prime D prime is shown with vertex A prime on ordered pair 1, 2 , vertex B prime on ordered pair 1, 4, vertex C prime on ordered 2, 1 and vertex D prime on ordered pair 2, 5. A 90 degrees counterclockwise rotation about the origin followed by a translation 1 unit to the left A translation 1 unit to the left, followed by a 90 degrees counterclockwise rotation about the origin A 270 degrees counterclockwise rotation about the origin followed by a translation 1 unit to the left A translation 1 unit to the left followed by a 270 degrees counterclockwise rotation about the origin

Answer 1

A 90 degrees counterclockwise rotation about the origin followed by a translation 1 unit to the left

Explanation:

The transformation of coordinates for figure ABCD ⇒ A'B'C'D' is ...

(x, y) ⇒ (-y-1, x)

__

We know the transformation ...

(x, y) ⇒ (-y, x)

represents a CCW rotation by 90°. And the transformation ...

(x, y) ⇒ (x-1, y)

represents a translation 1 unit left.

Combined, the rotation and translation produce the transformation described above. This figure has undergone ...

a 90° CCW rotation about the origin, followed by a translation 1 unit left.