Question

Verified answer please!

The figure shows two triangles on a coordinate grid: 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 triangle ABC is shown with vertex A on ordered pair 4, negative 1, vertex B on ordered pair 3, negative 1 and vertex C on ordered pair 3, negative 4. Another triangle A prime B prime C prime is shown with vertex A prime on ordered pair 1, 1, vertex B prime on ordered pair 2, 1, and vertex C prime on ordered pair 2, 4. What set of transformations is performed on triangle ABC to form triangle A'B'C'? A translation 5 units up followed by a 270 degree counterclockwise rotation about the origin A translation 5 units up followed by a 180 degree counterclockwise rotation about the origin A 270 degree counterclockwise rotation about the origin followed by a translation 5 units to the right A 180 degree counterclockwise rotation about the origin followed by a translation 5 units to the right

Answer 1

A 180 degree counterclockwise rotation about the origin followed by a translation 5 units to the right

Explanation:

The directed line segment AB points west (B is west of A). The directed line segment A'B' points east. A rotation of 180° is required to reverse the direction like that.

The two answer choices involving rotation of 180° give you the option of selecting ...

• a vertical translation up before rotation, or
• a horizontal translation right after rotation.

Translation of the figure 5 units upward will put it in the first quadrant, and the rotation will put the final figure in the 3rd quadrant.

__

Rotation 180° will put the figure in the 2nd quadrant (A"B"C" in the attachment) and translation to the right will move it to the 1st quadrant. Of course, rotation 180° in either direction (CW or CCW) about the origin is the same as reflection across the origin. (It negates all of the coordinate values.)

Hence the appropriate description of transformations is ...

A 180° rotation about the origin followed by a translation right 5 units