1.34 – TWO REFLECTIONS WITH NONPARALLEL LINES After the previous lesson, your teammate asks, “What if the lines of reflection are not parallel? Is the result still a translation?” Find ∆EFG and lines v and w below.
Text of 1.7 What if it is Rotated? Pg. 28 Rigid Transformations: Rotations
1.7 What if it is Rotated? Pg. 28 Rigid Transformations: Rotations 1.7 What if it is Rotated?_ Rigid Transformations: Rotations Today you will learn more about reflections and learn about two new types of transformations: rotations. 1.34 TWO REFLECTIONS WITH NONPARALLEL LINES After the previous lesson, your teammate asks, What if the lines of reflection are not parallel? Is the result still a translation? Find EFG and lines v and w below. a. First visualize the result when EFG is reflected over v to form and then is reflected over w to form Do you think it will be another translation? b. Draw the resulting reflections below. Is the final image a translation of the original triangle? If not, describe the result. turned c. Amanda noticed that when the reflecting lines are not parallel, the original shape is rotated, or turned, to get the new image. For example, the diagram at right shows the result when an ice cream cone is rotated about a point. In part (a), the center of rotation is at point P, the point of intersection of the lines of reflection. Use a piece of tracing paper to test that can be obtained by rotating about point P. To do this, apply pressure on P so that the tracing paper can rotate about this point. Then turn your tracing paper until rests atop Geogebra Rotations 1.35 ROTATIONS ON A GRID Consider what you know about rotation, a motion that turns a shape about a point. Does it make any difference if a rotation is clockwise ( ) versus counterclockwise ( )? If so, when does it matter? Are there any circumstances when it does not matter? And are there any situations when the rotated image lies exactly on the original shape? Investigate these questions as you rotate the shapes below about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above. 1.36 ROTATION SYMMETRY In problem 1.48, you learned that many shapes have reflection symmetry. These shapes remain unaffected when they are reflected across a line of symmetry. However, some shapes remain unchanged when rotated about a point. a. Examine the shape at right. Can this shape be rotated so that its image has the same position and orientation as the original shape? Trace this shape on tracing paper and test your conclusion. If it is possible, where is the point of rotation? b. Jessica claims that she can rotate all shapes in such a way that they will not change. How does she do it? She rotates it a full circle of 360 c. Since all shapes can be rotated in a full circle without change, that is not a very special quality. However, the shape in part (a) above was special because it could be rotated less than a full circle and still remain unchanged. A shape with this quality is said to have rotation symmetry. But what shapes have rotation symmetry? Examine the shapes below and identify those that have rotation symmetry.