To find the point \( L \) that divides the segment \( AB \) in the ratio \( 1:3 \), we can use the section formula. The coordinates of points \( A \) and \( B \) are given as follows:
- \( A (0,0) \)
- \( B (-2,3) \)
When dividing a line segment in the ratio \( m:n \), the coordinates of the dividing point \( L \) can be calculated using the formula:
\[ L = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \]
For our case, we have \( m = 1 \) and \( n = 3 \). Substituting the coordinates of points \( A \) and \( B \):
- \( x_1 = 0 \)
- \( y_1 = 0 \)
- \( x_2 = -2 \)
- \( y_2 = 3 \)
Substituting into the section formula gives:
\[ L_x = \frac{1 \times (-2) + 3 \times 0}{1 + 3} = \frac{-2 + 0}{4} = \frac{-2}{4} = -\frac{1}{2} \]
\[ L_y = \frac{1 \times 3 + 3 \times 0}{1 + 3} = \frac{3 + 0}{4} = \frac{3}{4} \]
Thus, the coordinates of point \( L \) are:
\[ L = \left(-\frac{1}{2}, \frac{3}{4}\right) \]
Therefore, the correct answer is:
b. \((-1/2, 3/4)\).