Step-by-step Solution:

The area of a triangle formed by joining the midpoints of two sides to the common vertex is exactly \( \frac{1}{4} \) of the area of the entire original triangle.\n\nLet the given vertex be \( A(1, 2) \). The mid-points are \( M_1(-1, 1) \) and \( M_2(2, 3) \).\nThe area of the small triangle formed by \( A \), \( M_1 \), and \( M_2 \) is:\n\[ \text{Area} = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| \]\n\[ = \frac{1}{2} |1(1 - 3) + (-1)(3 - 2) + 2(2 - 1)| \]\n\[ = \frac{1}{2} |-2 - 1 + 2| = \frac{1}{2} |-1| = 0.5 \]\n\nThe area of the original large triangle is \( 4 \times \text{Area of the small triangle} \).\n\[ \text{Total Area} = 4 \times 0.5 = 2 \text{ square units} \]