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

graph of triangle ABC in quadrant 4 and a second polygon A prime B prime C prime in quadrant 3
90° clockwise rotation
90° counterclockwise rotation
180° clockwise rotation
360° counterclockwise rotation

1 answer

To determine the direction and angle of rotation from triangle ABC in quadrant IV to triangle A'B'C' in quadrant III, we need to consider the positions of the triangles.

  1. Identify the movement from quadrant IV to quadrant III: A point in quadrant IV has a positive x-coordinate and a negative y-coordinate. A point in quadrant III has both x and y coordinates negative. Thus, any point moving from quadrant IV to quadrant III must move to the left (decrease x) and upwards (increase y).

  2. Determine the type of rotation:

    • A 90° clockwise rotation would move a point from quadrant IV to quadrant I.
    • A 90° counterclockwise rotation would move a point from quadrant IV to quadrant III.
    • A 180° rotation, regardless of direction, would move a point from quadrant IV to quadrant II.
    • A 360° rotation returns the point to its original position.

  3. Conclusion: Since the triangles are moving from quadrant IV to quadrant III, this corresponds to a 90° counterclockwise rotation.

Therefore, the answer is 90° counterclockwise rotation.