Composition of Transformations 1
Translation (4,4), reflect over the y-axis, rotation 90 degrees
How to identify a composition of transformations 1:
You can identify a composition of transformations of an image without using a coordinate graph or grid. First, you have to figure out how any point in the image moved from the pre-image to the image. For this example, I will use D and D'. If there was no grid you could figure out that this was a rotation 90 because there is a point of rotation which is E (located at (0,0) or the origin). You can figure out that it is a 90 rotation because if you connected D to E and D' to E and measure the angle, it would be 90. That is how you could figure out the first transformation without using a grid. For the second transformation, we will be looking at how D' moves to D''. The transformation is a reflection over the y-axis because D' and D'' are both equidistance from the figure and it's reflection and because the line of reflection forms a 90 angle with any segment connecting any point on the pre-image with it's image. That is how you could prove that the second transformation is a reflection over the y-axis. You could prove the third and last transformation, by looking at how D'' moves to D'''. The transformation is a translation because the the image moves to the right five and up one for each vertex in the image. There is also a vector which could help you realize that a translation is taking place. This is a translation and not a reflection or rotation because the image did not reflect over any line or rotate at all. Therefore, the transformation is a translation that moves . It goes to the right five points and up one point.That is how you could identify a composition of transformations without using a coordinate plane or grid.