Lines And Angles

The line passes through , so the parametric equations for line can be written as: Now, consider the first line: Let the common ratio for this line be . So, we can write the parametric equations for this line as: Now, consider the second line: Let the common ratio for this line be . So, we can write the parametric equations for this line as: We now need to find the value of where line intersects the two given lines.
The parametric equations of line and the first line give us a system of equations.
Similarly, the parametric equations of line and the second line also give us another system of equations.
Solving these equations yields the value of , and the corresponding point on line .
After solving the system, we find that the point lies on the line , as this point satisfies both the intersection conditions.
Thus, the correct answer is: