The midpoint of start overline, AB, end overline
AB
is M, left parenthesis, 1, comma, minus, 5, right parenthesisM(1,−5). If the coordinates of AA are left parenthesis, minus, 2, comma, minus, 3, right parenthesis(−2,−3), what are the coordinates of BB?

The midpoint formula is given by:

\[
M = \left( \frac{x_A + x_B}{2}, \frac{y_A + y_B}{2} \right)
\]

Where:
- \( M(1, -5) \) is the midpoint,
- \( A(-2, -3) \) are the coordinates of point A,
- \( B(x_B, y_B) \) are the unknown coordinates of point B.

Now, we will use the midpoint formula to find the coordinates of \( B(x_B, y_B) \).

### Step 1: Set up equations for the coordinates.

For the x-coordinate:

\[
\frac{x_A + x_B}{2} = 1
\]
\[
\frac{-2 + x_B}{2} = 1
\]
Multiplying both sides by 2:
\[
-2 + x_B = 2
\]
Solving for \( x_B \):
\[
x_B = 4
\]

For the y-coordinate:

\[
\frac{y_A + y_B}{2} = -5
\]
\[
\frac{-3 + y_B}{2} = -5
\]
Multiplying both sides by 2:
\[
-3 + y_B = -10
\]
Solving for \( y_B \):
\[
y_B = -7
\]

### Conclusion:
The coordinates of point \( B \) are \( B(4, -7) \).

Would you like more details on how the midpoint formula works or any further explanation?

Here are 5 related questions to expand on this concept:

1. What is the formula for the distance between two points?
2. How would the formula change if we were working in 3D space?
3. How do you find the slope of a line passing through two points?
4. If you know the midpoint and one endpoint, how can you find the other endpoint geometrically?
5. How does the midpoint formula relate to the concept of averages?

**Tip:** When working with midpoint problems, remember that the midpoint formula is essentially the average of the coordinates of the two points.

The midpoint of AB is M(1,−5). If the coordinates of A are (−2,−3), what are the coordinates of B?

Learn how to find the coordinates of point B given the midpoint M(1,−5) and point A(−2,−3). This problem demonstrates the use of the midpoint formula and is suitable for students in Grades 8-10.

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