The original expression is $$\frac{x+y}{2a} \cdot 1 \frac{2}{7}$$. This can be rewritten as $$\frac{x+y}{2a} \cdot \frac{9}{7}$$.
Let's analyze the options:
1. $$\frac{x+y}{2a} \cdot 1 \cdot \frac{2}{7}$$ is incorrect because it implies multiplication by 1 and then by 2/7, not by 9/7.
2. $$\frac{x+y}{2a} \cdot 1 + \frac{2}{7}$$ is incorrect due to the addition.
3. $$\frac{x+y}{2a} \cdot (1 + \frac{2}{7})$$ is incorrect as it implies multiplication by the sum, not by the mixed number.
4. $$\frac{x+y}{2a} \cdot (1 \frac{2}{7})$$ is correct because $$1 \frac{2}{7}$$ is equivalent to $$\frac{9}{7}$$.
5. $$\frac{x+y}{2a} \cdot (1+2)/7$$ is incorrect as it implies multiplication by 3/7.
6. $$\frac{x+y}{2a} \cdot (1+\frac{2}{7})$$ is incorrect as it implies multiplication by the sum, not by the mixed number. However, the OCR for this option is $$(x+y)/(2*a)*(1+2/7)$$, which is equivalent to $$\frac{x+y}{2a} \cdot (1+\frac{2}{7}) = \frac{x+y}{2a} \cdot \frac{9}{7}$$. This is a correct representation.
Therefore, the correct options are: (x+y)/(2*a)*(1 2/7) and (x+y)/(2*a)*(1+2/7).