Which Composition Of Similarity Transformations Maps Polygon ABCD To Polygon A’b’c’d’?

Which Composition Of Similarity Transformations Maps Polygon ABCD To Polygon A’b’c’d’?

To map one polygon onto another using similarity transformations, it is usually necessary to use a combination of transformations. Here are some multiple-choice options that could be possible answers to this question:

1. A translation followed by a rotation
2. A dilation followed by a translation
3. A rotation followed by a dilation
4. A dilation followed by a rotation

Answer:

In this case, it is impossible to accurately choose one correct option for further consideration without possessing more information about polygons ABCD and A’B’C’D’. However, let us explain one of the possible combinations and how it can be used Two components of metal halide lamps, mercury and halide, are combined along with a third component which is tungsten. Let’s focus on option 2: A dilation followed by a translation.

Translation and dilation are two similar transformations where the latter one along with the former one can move and enlarge polygon ABCD onto polygon A’B’C’D’ if the two polygons are of the same shape but of different scales and orientations. In this case, therefore, the dilation will first alter the size of polygon ABCD to that of A’B’C’D’ But hold the shape. Next, the translation would scale the resized polygon, to move it to the right position as being in A’B’C’D’. For example, let polygon ABCD be constructed like a square with a side length of 2 units and located in the coordinate plane with its vertices all at the coordinates of the origin at point 0. If A’B’C’D’ is the similar square of side 4 units, centred at (3,5), the transformation would take place in two stages. First, a dilation with scale factor 2 would enlarge ABCD to correspond to the size of A’B’C’D’. Subsequently, a translation of 3 units right and 5 units up would relocate the enlarged visible polygon to the right place (Myassignmenthelp.com, 2024). These transformations collectively maintain the angle measure of the polygon and scale as well as translate the figure; all of which is encapsulated in a similarity transformation.