The coordinates of the endpoints of $$ \overline{T U} $$ are $$ T(2,7) $$ and $$ U(17,-3) $$. Point $$ V $$ is on $$ \overline{T U} $$ and divides it such that $$ T V: U V $$ is $$ 1: 4 $$. What are the coordinates of $$ V $$ ? Write your answers as integers or decimals.

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To find the coordinates of point $$ V $$ that divides the segment $$ \overline{T U} $$ in the ratio $$ TV : UV = 1 : 4 $$, we can use the section formula for internal division.

Given:
- Coordinates of $$ T $$ are $$ (2, 7) $$.
- Coordinates of $$ U $$ are $$ (17, -3) $$.

The section formula for a point $$ V $$ dividing the line segment $$ \overline{T U} $$ in the ratio $$ m : n $$ is:

$$
V = \left( \frac{m x_2 + n x_1}{m + n}, \frac{m y_2 + n y_1}{m + n} \right)
$$

Here, $$ m = 1 $$ and $$ n = 4 $$. Plugging in the values:

$$
V_x = \frac{1 \times 17 + 4 \times 2}{1 + 4} = \frac{17 + 8}{5} = \frac{25}{5} = 5
$$

$$
V_y = \frac{1 \times (-3) + 4 \times 7}{1 + 4} = \frac{-3 + 28}{5} = \frac{25}{5} = 5
$$

Therefore, the coordinates of $$ V $$ are $$ (5, 5) $$.

**Answer:**  
$$V$$ has coordinates $$ (5,\ 5) $$.
The coordinates of $$ V $$ are $$ (5, 5) $$.

The coordinates of the endpoints of \( \overline{T U} \) are \( T(2,7) \) and \( U(17,-3) \). Point \( V \) is on \( \overline{T U} \) and divides it such that \( T V: U V \) is \( 1: 4 \). What are the coordinates of \( V \) ? Write your answers as integers or decimals.

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