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

Graph of triangle ABC in quadrant 4 with point A at 1 comma negative 3. A second polygon A prime B prime C prime in quadrant 3 with point A prime at negative 3 comma negative 1.
180° counterclockwise rotation
90° counterclockwise rotation
90° clockwise rotation
180° clockwise rotation

1 answer

To determine the direction and angle of rotation between triangle ABC and triangle A'B'C', we can analyze the coordinates of the points given.

  1. Point A (1, -3) rotates to Point A' (-3, -1).
  2. We need to find out how to transform point A to get to point A'.

Analyzing the Rotation:

  • 180° Rotation: A point (x, y) rotated 180° around the origin becomes (-x, -y).

    • For point A (1, -3), the 180° rotated point is (-1, 3), which is not point A' (-3, -1).

  • 90° Counterclockwise Rotation: A point (x, y) rotated 90° counterclockwise becomes (-y, x).

    • For point A (1, -3), it becomes (3, 1), which is not point A' (-3, -1).

  • 90° Clockwise Rotation: A point (x, y) rotated 90° clockwise becomes (y, -x).

    • For point A (1, -3), it becomes (-3, -1), which matches point A' (-3, -1).

  • 180° Clockwise Rotation: A point (x, y) rotated 180° clockwise behaves the same as counterclockwise: it becomes (-x, -y).

    • As already calculated, this does not match.

Conclusion:

The transformation from point A to point A' is a 90° clockwise rotation.