Determine the rotation image of figure below if it is rotated 270 degrees clockwise about point A.
The Correct Answer and Explanation is:
The correct answer is the fourth option in the list.
To determine the correct rotated image, we must follow the instructions to rotate the original figure 270 degrees clockwise around point A. A rotation is a rigid transformation in geometry, meaning the shape and size of the figure remain identical, while its orientation changes based on the specified angle and center of rotation.
Visualizing a 270-degree turn can be complex, so a helpful strategy is to recognize that a 270-degree clockwise rotation is equivalent to a 90-degree counter-clockwise rotation. Both transformations will result in the exact same final position. Thinking about a single 90-degree turn is often simpler.
Let’s trace the movement of the figure using this 90-degree counter-clockwise rotation. The original figure is positioned with its unique wavy side on the left. The center of rotation, point A, is located in the middle of the bottom straight edge.
When we rotate the figure 90 degrees counter-clockwise about point A, every part of the figure pivots. The bottom edge, which holds point A, swings upwards and to the right, becoming the new vertical edge on the right side of the figure. Consequently, point A will now be at the midpoint of this right edge. The wavy side, which was originally on the left, rotates downwards to become the new bottom edge. The original top straight edge moves to become the new left edge, and the original right straight edge moves to become the new top edge.
After completing this rotation, the figure’s final orientation has its wavy side along the bottom and its formerly bottom edge, with point A, now forming the right side. When we examine the multiple-choice options provided, the fourth figure perfectly matches this description. It shows the correct orientation of the wavy side and the correct placement of point A on the right side, confirming it is the accurate result of the rotation.
