Composition of Transformations 2
Reflect over the y axis, Rotate around point G 180 degrees, Rotate 180 degrees from Point F
Identifying a composition of transformations 2:
You can identify a composition of transformations without using a coordinate grid or graph. First, you have to find the pre-image and the image that will be created using that image (A to A'). In this example, C and C' are equidistance from the point of rotation F. As a result it could be a rotation because it has a center point, each vertex is moved the same degree, and each vertex is moved the same direction around the center of rotation. Each vertex is the same distance from the center. You can find the angle of rotation by connecting C to F and C' to F and calculate the angle measure. It should be 180, which proves that the first transformation in this composition is a rotation around point F 180. After you figure out the first transformation without using a graph, you do the same to the second transformation which is from C' to C''. The second transformation is a rotation around point G 180 because each vertex moved the same degree and direction around the center of rotation. Each vertex must be the same distance from the center. In this image, you could tell that a rotation has occurred without using a grid or coordinate plane by realizing that there is a center of rotation (which is a fixed point) that when you draw a line from vertex C' to point G and C" to G, it creates a 90 degree angle which represents a rotation 90 degrees counter clockwise. After figuring out that the second transformation is a rotation, you figure out the third transformation from looking at how C" moved to C"'. This transformation is a reflection across the y-axis because the line of reflection is equidistant from the figure and it's reflection. The line of reflection also forms a 90 angle with any segment connecting any point on the pre-image with it's image. That is how you could identify a reflection across the y-axis without a coordinate graph or grid. As a result, you can identify a composition of transformations without using a coordinate graph or grid.