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Given AXYZ, line n with equation x = -2, and line p with equation x = 2, write a translation that is equivalent to R n• Rp.

User Avnic
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Final answer:

The equivalent translation to combined reflections across lines n and p, which are parallel and 4 units apart, is a translation of 8 units to the right, represented as T(8,0).

Step-by-step explanation:

The student has asked about a translation that is equivalent to Rn ⋅ Rp, where Rn is a reflection across the line n with equation x = -2, and Rp is a reflection across the line p with equation x = 2.

When we reflect a shape across two parallel lines that are equidistant from a central line, the effect is the same as translating the shape twice the distance between those lines.

In this case, the distance between lines n and p is 4 units (from -2 to 2). Therefore, the equivalent single translation for Rn ⋅ Rp would be a translation of 8 units to the right, often written as T(8,0).

User Whamsicore
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