3. The midpoint of $$ \overline{\mathrm{AB}} $$ is $$ M(-4,4) $$. If the coordinates of $$ A $$ are $$ (-6,1) $$, what are the coordinates of $$ B $$ ?

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To find the coordinates of point $$ B $$, we can use the formula for the midpoint of a line segment. The midpoint $$ M $$ of a line segment connecting points $$ A(x_1, y_1) $$ and $$ B(x_2, y_2) $$ is given by:

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

In this case, we know the coordinates of point $$ A $$ are $$ (-6, 1) $$ and the coordinates of the midpoint $$ M $$ are $$ (-4, 4) $$. We need to find the coordinates of point $$ B $$, which we can denote as $$ (x_2, y_2) $$.

Using the midpoint formula, we can set up the following equations based on the coordinates of $$ M $$:

1. For the x-coordinates:
$$
\frac{-6 + x_2}{2} = -4
$$

2. For the y-coordinates:
$$
\frac{1 + y_2}{2} = 4
$$

Now, we will solve these equations one by one.

**Solving for $$ x_2 $$:**

Starting with the first equation:
$$
\frac{-6 + x_2}{2} = -4
$$

Multiply both sides by 2:
$$
-6 + x_2 = -8
$$

Add 6 to both sides:
$$
x_2 = -8 + 6
$$
$$
x_2 = -2
$$

**Solving for $$ y_2 $$:**

Now, using the second equation:
$$
\frac{1 + y_2}{2} = 4
$$

Multiply both sides by 2:
$$
1 + y_2 = 8
$$

Subtract 1 from both sides:
$$
y_2 = 8 - 1
$$
$$
y_2 = 7
$$

Thus, the coordinates of point $$ B $$ are:
$$
B(-2, 7)
$$

Therefore, the final answer is:
$$
\boxed{(-2, 7)}
$$
The coordinates of point $$ B $$ are $$ (-2, 7) $$.

3. The midpoint of \( \overline{\mathrm{AB}} \) is \( M(-4,4) \). If the coordinates of \( A \) are \( (-6,1) \), what are the coordinates of \( B \) ?

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