To find the coordinates of point V that divides segment TU in the ratio 7:2, we can use the section formula. The coordinates of point V can be calculated using the formula:
\[ V_x = \frac{m \cdot x_2 + n \cdot x_1}{m + n} \] \[ V_y = \frac{m \cdot y_2 + n \cdot y_1}{m + n} \]
where \( m \) and \( n \) are the parts of the ratio, and \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of points T and U.
Given:
- \( T(2, 4) \) and \( U(11, 13) \)
- The ratio \( TV:UV = 7:2 \), so \( m = 7 \) and \( n = 2 \)
Now, substituting the values into the section formula:
- Calculate \( V_x \):
\[ V_x = \frac{7 \cdot 11 + 2 \cdot 2}{7 + 2} = \frac{77 + 4}{9} = \frac{81}{9} = 9 \]
- Calculate \( V_y \):
\[ V_y = \frac{7 \cdot 13 + 2 \cdot 4}{7 + 2} = \frac{91 + 8}{9} = \frac{99}{9} = 11 \]
Thus, the coordinates of point V are:
\[ V(9, 11) \]
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