8.5 Transformational Geometry, Symmetry, and Tessellations 507 Now that we have an intuitive idea of how to determine a rotation, we give the definition of rotation. Definition: Rotation A rotation is a rigid motion performed by rotating a geometric figure in the plane about a specific point, called the rotation point or the center of rotation. The angle through which the object is rotated is called the angle of rotation. We will measure angles of rotation using degrees. In mathematics, generally, counterclockwise angles have positive degree measures and clockwise angles have negative degree measures. A B C D P Figure 8.62 Example 4 A Rotated Rectangle Given rectangle ABCD and rotation point P, shown in Fig. 8.62, construct rectangles that result from rotations through a) 90.° b) 180 .° c) 270.° Solution a) First, since 90 is a positive number, we will rotate the figure in a counterclockwise direction. We also note that the rotated rectangle will be the same size and shape as rectangle ABCD. To get an idea of what the rotated rectangle will look like, pick up this book or a printed page, and rotate it counterclockwise 90 .° If you are viewing this page electronically, print out the page and then rotate the page 90 .° Figure 8.63 shows rectangle ABCD and rectangle A BC D, ′ ′ ′ ′ which is rectangle ABCD rotated 90° about point P. Notice how line segment AB in rectangle ABCD is horizontal, but in the rotated rectangle in Fig. 8.63 line segment A B′ ′ is vertical. Also notice that in rectangle ABCD vertex D is 3 units to the right and 1 unit above rotation point P, but in the rotated rectangle, vertex D′ is 3 units above and 1 unit to the left of rotation point P. A B C D P Bc Cc Dc Ac Figure 8.63 b) To gain some perspective on a 180° rotation, again pick up this book or a printed page, but this time rotate it 180° in the counterclockwise direction. The rotated rectangle A B C D ″ ″ ″ ″ is shown along with the rectangle ABCD in Fig. 8.64.
RkJQdWJsaXNoZXIy NjM5ODQ=