Option 2 : (1, 2)

**Given:**

(x_{1}, y_{1}) = (3, 1), (x_{2}, y_{2}) = (2, 3) and (x_{3}, y_{3}) = (-2, 2)

**Concept:**

Use of formula for calculating the centroid of a triangle.

**Formula used:**

\({\rm{X}}\left( {{\rm{coordinate\;of\;a\;centroid}}} \right) = \frac{{{{\rm{x}}_1} + {{\rm{x}}_2} + {{\rm{x}}_3}}}{3}\)

\({\rm{Y}}\left( {{\rm{coordinate\;of\;a\;centroid}}} \right) = \frac{{{{\rm{y}}_1} + {{\rm{y}}_2} + {{\rm{y}}_3}}}{3}\)

**Calculation:**

\({\rm{X}} = \frac{{3 + 2 + \left( { - 2} \right)}}{3}\)

⇒ X = 1

\({\rm{Y}} = \frac{{1 + 3 + 2}}{3}\)

⇒ Y = 2