To find the coordinates of point \( X \) on segment \( AB \) that partitions the segment into the ratio \( AX:BX = 1:2 \), we can use the section formula.
Given points \( A(x_1, y_1) \) and \( B(x_2, y_2) \), the coordinates of point \( X \) that divides the segment \( AB \) in the ratio \( m:n \) are given by:
\[ X = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \]
Here, the ratio \( AX:BX = 1:2 \) means \( m = 1 \) and \( n = 2 \).
Let's assume the coordinates of points \( A \) and \( B \) are \( A(x_1, y_1) \) and \( B(x_2, y_2) \). You will need to use their specific coordinates.
Since the exact coordinates of points \( A \) and \( B \) were not provided in your query, I will demonstrate how to apply the formula:
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Determine Coordinates:
- Let \( A(x_1, y_1) = (x_1, y_1) \)
- Let \( B(x_2, y_2) = (x_2, y_2) \)
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Apply the Section Formula: \[ X = \left( \frac{1 \cdot x_2 + 2 \cdot x_1}{1+2}, \frac{1 \cdot y_2 + 2 \cdot y_1}{1+2} \right) \] \[ X = \left( \frac{x_2 + 2x_1}{3}, \frac{y_2 + 2y_1}{3} \right) \]
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Identify Results:
- Substitute the coordinates of \( A \) and \( B \) into the formula to find the precise coordinates of \( X \).
After doing this with the provided coordinates, you will yield your point \( X \).
Feel free to provide the specific coordinates of \( A \) and \( B \) if you have them, and I can calculate \( X \). Alternatively, you can check the possible response choices against your calculations to find the correct one.
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