BC 270 degrees clockwise around B. What would it look like when you rotate the four triangles 90 degrees clockwise round B? 80 degrees? 70 degrees clockwise?
Rotate triangle ABC 90 degrees clockwise around B. Rotate triangle ABC 180 degrees clockwise round B. Rotate triangle ABC 270 degrees clockwise around B. What would it look like when you rotate the four triangles 90 degrees clockwise round B? 80 degrees? 70 degrees
The Correct Answer and Explanation is:
To answer this question, we need to understand what it means to rotate triangle ABC around point B. When we rotate a shape around a point, each vertex of the shape turns around that point by the given angle, maintaining its distance from that point. In this case, B stays in the same position because it is the center of rotation.
Rotating Triangle ABC Clockwise Around Point B
Let us consider triangle ABC with vertices A, B, and C. When we rotate triangle ABC around point B:
- 90 degrees clockwise: Point A and point C both move 90 degrees clockwise around point B. This places A and C in new positions that form a triangle that looks like the original triangle turned one quarter of a full turn to the right.
- 180 degrees clockwise: Point A and point C both move 180 degrees around point B. The triangle now appears upside down compared to the original, because it has been rotated halfway around a circle.
- 270 degrees clockwise: This is the same as rotating 90 degrees counterclockwise. The triangle now appears turned three-quarters of a full turn, and the orientation is very different from the original.
Rotating Four Triangles Around B
If you have four copies of triangle ABC placed together with point B as the shared center, and you rotate all of them 90 degrees clockwise, each triangle moves into the place of the next one in a clockwise direction, forming a circular motion around point B.
If you rotate the four triangles 80 degrees or 70 degrees clockwise around point B, they will not fall into perfect positions. They will appear slightly shifted and misaligned. Each triangle will move less than a quarter turn, making them look slightly off from where they started. The shape becomes less symmetric and more scattered compared to the neat 90-degree rotation.
In summary, rotating by 90, 180, or 270 degrees results in well-defined triangle positions, while rotating by 80 or 70 degrees gives misaligned or intermediate positions.
