which describes the compositions of 3 reflections in three distinct line, two of which are paralell?
To understand the composition of three reflections in three distinct lines, two of which are parallel, we need to consider the properties of reflections and how they interact with parallel lines.
First, let's review what a reflection is. In mathematics, a reflection is a transformation that "flips" an object over a line, known as the line of reflection. When an object is reflected, it creates a mirror image of itself.
Now, let's consider three distinct lines: line A, line B, and line C. Of these three lines, lines A and B are parallel.
To perform the composition of three reflections, we will reflect an object successively over these three lines. Let's assume we have an initial object, such as a point or a shape, which we will refer to as object O.
1. Reflection over line A: Start by reflecting object O over line A, resulting in a new object O1.
2. Reflection over line B: Take the object O1 and reflect it over line B, resulting in a new object O2.
3. Reflection over line C: Finally, take object O2 and reflect it over line C to obtain the composition, resulting in a final object O3.
It's important to note that the composition of reflections is the same regardless of whether the lines of reflection are parallel or not. The order of reflections matters, and in this case, we performed the reflections in the order A, B, and then C.
To summarize, the composition of three reflections in three distinct lines, two of which are parallel, involves reflecting an initial object O successively over each line to obtain a final object O3.