The midpoint of start overline, AB, end overlineAB is M, left parenthesis, minus, 2, comma, 4, right parenthesis*M*(−2,4). If the coordinates of A*A* are left parenthesis, minus, 1, comma, 5, right parenthesis(−1,5), what are the coordinates of B*B*?

To find the coordinates of point \( B \), we can use the midpoint formula.

The midpoint \( M(x_m, y_m) \) of a line segment connecting two points \( A(x_a, y_a) \) and \( B(x_b, y_b) \) is given by the formula:

\[
M = \left( \frac{x_a + x_b}{2}, \frac{y_a + y_b}{2} \right)
\]

We know:
- The midpoint \( M = (-2, 4) \),
- The coordinates of point \( A = (-1, 5) \).

Let the coordinates of point \( B \) be \( (x_b, y_b) \).

Using the midpoint formula, we can set up two equations:

1. For the \( x \)-coordinates:
\[
\frac{-1 + x_b}{2} = -2
\]
Multiplying both sides by 2:
\[
-1 + x_b = -4
\]
Solving for \( x_b \):
\[
x_b = -4 + 1 = -3
\]

2. For the \( y \)-coordinates:
\[
\frac{5 + y_b}{2} = 4
\]
Multiplying both sides by 2:
\[
5 + y_b = 8
\]
Solving for \( y_b \):
\[
y_b = 8 - 5 = 3
\]

Thus, the coordinates of point \( B \) are \( (-3, 3) \).

Would you like a detailed explanation of the midpoint formula or have any other questions?

Here are 5 related questions:
1. What is the distance between points \( A \) and \( B \)?
2. How can you find the slope of line segment \( AB \)?
3. If the line segment \( AB \) is extended beyond point \( B \), what would the coordinates of a point \( C \) be, such that \( B \) is the midpoint of \( AC \)?
4. How do you find the equation of the line passing through points \( A \) and \( B \)?
5. What is the general formula for finding the center of mass of two points in a plane?

**Tip:** The midpoint formula is very useful in geometry, especially when dividing line segments in half or finding the center between two points.

The midpoint of AB is M(−2, 4). If the coordinates of A are (−1, 5), what are the coordinates of B?

Learn how to find the coordinates of point B given the midpoint M(−2, 4) and point A(−1, 5) using the midpoint formula. This problem covers key concepts in geometry and coordinate geometry. Suitable for students in Grades 8-10.

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