To find the coordinates of point B, given that M is the midpoint of segment AB and you have the coordinates of A, you can use the midpoint formula:

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

Given:

• $M = (-6, 3)$
• $A = (-5, 5)$

Let the coordinates of $B$ be $(x_2, y_2)$.

Using the midpoint formula:

$\left( \frac{-5 + x_2}{2}, \frac{5 + y_2}{2} \right) = (-6, 3)$

This gives us two equations:

1. $\frac{-5 + x_2}{2} = -6$
2. $\frac{5 + y_2}{2} = 3$

Solving for $x_2$:

$\frac{-5 + x_2}{2} = -6$ Multiply both sides by 2: $-5 + x_2 = -12$ Add 5 to both sides: $x_2 = -7$

Solving for $y_2$:

$\frac{5 + y_2}{2} = 3$ Multiply both sides by 2: $5 + y_2 = 6$ Subtract 5 from both sides: $y_2 = 1$

Therefore, the coordinates of point $B$ are $(-7, 1)$.

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you find the midpoint if both points $A$ and $B$ are known?
2. What is the formula to find the distance between two points in a coordinate plane?
3. How do you determine the slope of a line segment given two points?
4. What are the coordinates of the midpoint if $B = (x_2, y_2)$ and $M = (2, -3)$?
5. If the coordinates of $A$ were different, how would that affect the coordinates of $B$?

Tip: When solving for unknowns using the midpoint formula, it's crucial to correctly isolate the variables step by step to avoid errors.