To find the coordinates of point \( X \) that partitions segment \( AB \) in the ratio \( AX:BX = 1:2 \), we can use the section formula.
Let the coordinates of \( A \) be \( (x_1, y_1) \) and the coordinates of \( B \) be \( (x_2, y_2) \). According to the section formula, the coordinates of point \( X \) that divides the segment \( AB \) internally in the ratio \( m:n \) (where \( m = 1 \) and \( n = 2 \) in this case) can be found using the formulas:
\[ X_x = \frac{mx_2 + nx_1}{m+n} \] \[ X_y = \frac{my_2 + ny_1}{m+n} \]
Step 1: Identify coordinates of points A and B
Assuming point \( A = (x_1, y_1) \) and point \( B = (x_2, y_2) \) we need the actual coordinates to apply the formula. However, since you haven't provided these coordinates, let's assume you have them as follows:
Assuming:
- \( A(-4, -10) \) (i.e., coordinates of A)
- \( B(-3, 8) \) (i.e., coordinates of B)
Step 2: Compute coordinates of point X
Using the section formula to find \( X \):
\[ X_x = \frac{1*(-3) + 2*(-4)}{1 + 2} = \frac{-3 - 8}{3} = \frac{-11}{3} \]
\[ X_y = \frac{18 + 2(-10)}{1 + 2} = \frac{8 - 20}{3} = \frac{-12}{3} = -4 \]
Thus, the coordinates of point \( X \) are:
\[ X\left( -\frac{11}{3}, -4 \right) \]
However, if you have specific coordinates for points \( A \) and \( B \), please provide them, and I can confirm the calculations. Based on the responses you have provided, the values of \( X \) that you are looking for should align with the computed coordinates of \( X \).
Among the mentioned options, none explicitly match the simple division, hence feel free to specify the coordinates of \( A \) and \( B \) for accurate computation.
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