To find the coordinates of point X that partitions the directed segment AB in the ratio of 1:2, we can use the section formula. The section formula states that if a point \( P(x, y) \) divides the line segment joining points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in the ratio \( m:n \), then the coordinates of point \( P \) can be calculated as follows:
\[ P\left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \]
Here, \( A \) and \( B \) are the endpoints of the segment, and \( m:n = 1:2 \).
To apply this formula, we need the coordinates of points \( A \) and \( B \). Since the coordinates of points \( A \) and \( B \) are not provided in your question, please share those coordinates so we can calculate the coordinates of point \( X \).