The midpoint of AB is M(-6,3) if the coordinates of A are (-5,5) what are the coordinates of B

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.

The midpoint of AB is M(-6,3) if the coordinates of A are (-5,5) what are the coordinates of B?

Solve the problem of finding the coordinates of point B when the midpoint M(-6,3) and point A(-5,5) are given. Learn how to apply the midpoint formula step by step in this geometry problem suitable for students in Grades 6-8.

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