To understand the translation equivalent to the composition of the reflections \( R_p \) and \( R_q \), we first need to analyze what these reflections represent.
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Line \( p \) (x = 2): A reflection across the vertical line \( x = 2 \) will move any point \( (x, y) \) to the point \( (4 - x, y) \). This is because the distance from a point \( (x, y) \) to the line \( x = 2 \) is \( |x - 2| \), and the reflected point will be the same distance on the other side of the line.
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Line \( q \) (x = -1): Similarly, a reflection across the vertical line \( x = -1 \) moves any point \( (x, y) \) to the point \( (-2 - x, y) \).
Now, let's analyze the composition \( (R_p \circ R_q)(\triangle ABC) \):
First, apply \( R_q \) to a generic point \( (x, y) \): \[ R_q: (x, y) \to (-2 - x, y). \]
Next, apply \( R_p \) to the result of \( R_q \): Starting from point \( (-2 - x, y) \), we apply the reflection across \( x = 2 \): \[ R_p: (-2 - x, y) \to (4 - (-2 - x), y) = (4 + 2 + x, y) = (6 + x, y). \]
Thus, the net effect of \( (R_p \circ R_q) \) on the point \( (x, y) \) is: \[ (x, y) \to (6 + x, y), \] which indicates a translation of \( T(6, 0) \).
Therefore, the equivalent translation is \( \text{T}(6, 0) \).
This matches the selected option a. T(6,0), which is correct.