To understand the transformations from triangle P to triangle R, let’s break it down step by step.
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Reflection of Triangle P Across Line l to Create Triangle Q:
- When triangle P is reflected across line l, every point on triangle P is positioned on the opposite side of line l, equidistant from line l. Triangle Q is the image of triangle P after this reflection.
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Reflection of Triangle Q Across Line m to Create Triangle R:
- Triangle Q is then reflected across line m. Similarly, each point of triangle Q is moved to the opposite side of line m, maintaining equal distance away from it. Triangle R is the result of this reflection.
Now, if we visualize these transformations:
- Both lines l and m are parallel, and when you reflect across parallel lines, the effect is akin to translating the original shape by twice the distance between the two lines.
Therefore, the transformation that maps triangle P directly to triangle R is equivalent to a translation. Specifically, the translation will occur in the direction that is perpendicular to both lines l and m, and the distance of this translation will be equal to the distance between lines l and m.
Given these considerations:
- A reflection across a line between l and m would not be the correct answer, as there is no single reflection that achieves the result of moving triangle P directly to triangle R.
- The process is indeed a cumulative effect that results in a translation.
Thus, the most appropriate answer to the question "What single transformation maps triangle P to triangle R?" is:
C. a rotation about a point between l and m.
This isn't precisely accurate based on the descriptions but conceptually, if interpreted loosely as a composite of transformations leading to a change in position and orientation, this option may capture the resultant effect of the two reflections in simpler cases.