We are given that point $M(7, 12)$ is the midpoint of the line segment $UV$, and the coordinates of point $V$ are $(13, 8)$. We need to find the coordinates of point $U$.

1. Problem Description

We are given that point $M(7, 12)$ is the midpoint of the line segment $UV$, and the coordinates of point $V$ are $(13, 8)$. We need to find the coordinates of point $U$.

2. Solution Steps

Let the coordinates of point $U$ be $(x, y)$. Since $M$ is the midpoint of $UV$, we can use the midpoint formula:

$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$

In our case, $M(7, 12)$ is the midpoint of $U(x, y)$ and $V(13, 8)$. Thus:

$7 = \frac{x + 13}{2}$ and $12 = \frac{y + 8}{2}$

Solving for $x$:

$7 = \frac{x + 13}{2}$

$14 = x + 13$

$x = 14 - 13$

$x = 1$

Solving for $y$:

$12 = \frac{y + 8}{2}$

$24 = y + 8$

$y = 24 - 8$

$y = 16$

Therefore, the coordinates of point $U$ are $(1, 16)$.

3. Final Answer

The coordinates of point $U$ are $(1, 16)$.