Use the image to determine the direction and angle of rotation.

Question

Graph of polygon ABCD in quadrant 1 with point A at 1 comma 5. A second polygon A prime B prime C prime D prime in quadrant 3 with point A prime at negative 1 comma negative 5.
90° counterclockwise rotation
180° counterclockwise rotation
90° clockwise rotation
270° clockwise rotation

Answer 1

To determine the direction and angle of rotation from polygon ABCD to polygon A'B'C'D', let's first identify the coordinates of point A and its image A'.

Point A is at (1, 5) and its image A' is at (-1, -5).

1. Finding the rotation:

   • The point A (1, 5) is transformed into A' (-1, -5).
   • A rotation around the origin affects the coordinates of points.
   • A 90° counterclockwise rotation transforms a point (x, y) to (-y, x).
   • A 90° clockwise rotation transforms a point (x, y) to (y, -x).
   • A 180° rotation transforms (x, y) to (-x, -y).

2. Calculating the transformation:

   • Checking if it's a 180° rotation:
     • The coordinates of A (1, 5) after a 180° rotation: (-1, -5), which matches A' (-1, -5).

Since A (1, 5) fully aligns with A' (-1, -5) by 180° rotation, we conclude that the transformation from polygon ABCD to polygon A'B'C'D' is a:

180° counterclockwise rotation.