To find the coordinates of point $B$, we can use the midpoint formula:

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

where $M(-1, 6)$ is the midpoint, $A(2, 8)$ are the coordinates of point $A$, and $B(x, y)$ are the coordinates of point $B$.

Let’s set up the equations:

1. For the x-coordinates:

$-1 = \frac{2 + x}{2}$

Multiplying both sides by 2:

$-2 = 2 + x$

Solving for $x$:

$x = -4$

2. For the y-coordinates:

$6 = \frac{8 + y}{2}$

Multiplying both sides by 2:

$12 = 8 + y$

Solving for $y$:

$y = 4$

So, the coordinates of point $B$ are:

$B(-4, 4)$

Would you like more details or have any questions?

Related Questions:

1. How do you find the midpoint if the coordinates of two points are known?
2. What is the significance of the midpoint in coordinate geometry?
3. Can the midpoint formula be used in three-dimensional space?
4. How can you verify if a point is the midpoint of a line segment?
5. What are some applications of the midpoint formula in real-world problems?

Tip:

Always double-check your work by substituting the coordinates back into the midpoint formula to ensure accuracy!