To find the coordinates of point $B$, given the midpoint $M(-2, 6)$ and point $A(-3, 8)$, we can use the midpoint formula:

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

Here, $M(-2, 6)$ is the midpoint, $A(-3, 8)$ is one endpoint, and $B(x_2, y_2)$ is the other endpoint. Plugging in the known values:

For the x-coordinate: $-2 = \frac{-3 + x_2}{2}$ Multiply both sides by 2: $-4 = -3 + x_2$ Add 3 to both sides: $x_2 = -1$

For the y-coordinate: $6 = \frac{8 + y_2}{2}$ Multiply both sides by 2: $12 = 8 + y_2$ Subtract 8 from both sides: $y_2 = 4$

So, the coordinates of point $B$ are $(-1, 4)$.

Would you like further details or have any questions?

Here are five related questions to expand your understanding:

1. How would you find the coordinates of $B$ if the midpoint and coordinates of $B$ were given?
2. What is the distance between points $A$ and $B$ in this problem?
3. Can you find the slope of the line segment $AB$ given the coordinates of $A$ and $B$?
4. How would the solution change if the coordinates of $M$ were not integers?
5. What is the geometric significance of a midpoint in a triangle?

Tip: When working with midpoints, always remember that the midpoint is the average of the coordinates of the two endpoints.