Point M is the midpoint of the line segment AB. The coordinates of point A are (5, 3), and the coordinates of point M are (11, 7). We need to find the coordinates of point B.

1. Problem Description

Point M is the midpoint of the line segment AB. The coordinates of point A are (5, 3), and the coordinates of point M are (11, 7). We need to find the coordinates of point B.

2. Solution Steps

Let the coordinates of point A be $(x_A, y_A)$ and the coordinates of point B be $(x_B, y_B)$. The coordinates of the midpoint M of the line segment AB are given by $(x_M, y_M)$, where

$x_M = \frac{x_A + x_B}{2}$

$y_M = \frac{y_A + y_B}{2}$

We are given that $x_A = 5$, $y_A = 3$, $x_M = 11$, and $y_M = 7$. We need to find $x_B$ and $y_B$.

Substituting the given values into the midpoint formulas, we get:

$11 = \frac{5 + x_B}{2}$

$7 = \frac{3 + y_B}{2}$

Now, we can solve for $x_B$ and $y_B$:

$22 = 5 + x_B$

$x_B = 22 - 5 = 17$

$14 = 3 + y_B$

$y_B = 14 - 3 = 11$

Therefore, the coordinates of point B are (17, 11).

3. Final Answer

The coordinates of point B are (17, 11).