To find the coordinates of point \( X \) on line segment \( AB \) such that the ratio of \( AX \) to \( XB \) is \( 3:5 \), we can use the section formula. The section formula states:
If a point \( X \) divides the line segment \( AB \) in the ratio \( m:n \), the coordinates of point \( X \) are given by:
\[ X\left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right) \]
In this case, the coordinates of point \( A \) are \( (-1, 2) \) and point \( B \) are \( (3, 6) \). The ratio \( AX:XB = 3:5 \) means \( m = 3 \) and \( n = 5 \).
Now, we can calculate the coordinates of point \( X \):
- \( x_1 = -1 \), \( y_1 = 2 \)
- \( x_2 = 3 \), \( y_2 = 6 \)
Substituting these values into the formula:
\[ X_x = \frac{3 \cdot 3 + 5 \cdot (-1)}{3 + 5} = \frac{9 - 5}{8} = \frac{4}{8} = \frac{1}{2} \]
\[ X_y = \frac{3 \cdot 6 + 5 \cdot 2}{3 + 5} = \frac{18 + 10}{8} = \frac{28}{8} = \frac{7}{2} \]
Thus, the coordinates of point \( X \) are:
\[ \left( \frac{1}{2}, \frac{7}{2} \right) \]
Since the question asks for the coordinates of point \( X \) such that the ratio of \( AX \) to \( XB \) is \( 3:5 \), the correct coordinates are: \[ \left( \frac{1}{2}, \frac{7}{2} \right) \]
This can also be interpreted as \( (0.5, 3.5) \).
None of the provided responses matches this result directly, as they instead use fraction forms. Therefore, based on the possible answers, the closest resemblance considering equivalent fractions would be related to \( \left( \frac{1}{2}, \frac{7}{2} \right) \), but none exactly match from the listed choices. Please double-check the options or the question’s demands for clarification if there's a specific revision needed.
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