\( A ( \frac { x _ { 1 } } { 3 } , - 4 y _ { 1 } ) \quad x = \frac { 2 } { 5 } \)

To solve the study problem, we need to find the value of \( x \) given the equation \( A \left( \frac { x _ { 1 } } { 3 }, - 4 y _ { 1 } \right) \) and the condition \( x = \frac { 2 } { 5 } \). However, the problem statement seems to be incomplete or possibly contains a typo. The variable \( x \) is mentioned twice, and it's not clear how it relates to the coordinates \( \left( \frac { x _ { 1 } } { 3 }, - 4 y _ { 1 } \right) \). Assuming that \( x \) refers to the first coordinate of point \( A \), we can set up the following equation: \[ x = \frac { x _ { 1 } } { 3 } \] Given that \( x = \frac { 2 } { 5 } \), we can solve for \( x _ { 1 } \) as follows: \[ \frac { 2 } { 5 } = \frac { x _ { 1 } } { 3 } \] To find \( x _ { 1 } \), we multiply both sides of the equation by 3: \[ x _ { 1 } = \frac { 2 } { 5 } \times 3 \] \[ x _ { 1 } = \frac { 6 } { 5 } \] So, the value of \( x _ { 1 } \) is \( \frac { 6 } { 5 } \). If this is the information you were looking for, then the problem is solved. If there is more to the problem or if there are additional conditions, please provide the full details so that we can solve it completely.