a To rotate a vertex, draw a segment from the vertex to the origin. Then use a protractor to draw a second congruent segment from the origin along the correct number of degrees on the protractor.
B
b The star has a point for every 45^(∘).
C
c What shape looks the same no matter how you turn it?
To rotate the figure 90^(∘) clockwise around the origin, we need a protractor. First, we draw segments from each vertex to the origin. Then, place the center of the protractor at the origin and line it up along one of the segments. By drawing a congruent segment from the origin and along the 90^(∘) mark on the protractor, we will have located one of the rotated points.
If we repeat this process for all vertices and connect the new points, we can draw the rotated figure.
The figure looks exactly the same as before. We would get the same result if we rotate the figure 45^(∘) and 180^(∘).
b From Part A, we know that when rotating the figure by 180^(∘), 90^(∘) and 45^(∘), the figure maps onto itself. If we place the protractor on the coordinate plane, we notice that at every 45^(∘), the figure repeats itself.
Therefore, the figure has a rotational symmetry of 45^(∘). This means we could also rotate it, for example, 135^(∘) and have it map onto itself.
c The only shape that does not change its appearance when rotated an arbitrary number of degrees is a circle. No matter how much you rotate a circle, it will always map onto itself.
