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

To find the coordinates of point \( B \), we can use the midpoint formula. The formula for the midpoint \( M(x_m, y_m) \) of a line segment with endpoints \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is:

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

We are given:

- Midpoint \( M(2, 4) \)
- Point \( A(-1, 5) \)

Let the coordinates of point \( B \) be \( (x_2, y_2) \). Using the midpoint formula:

\[
\frac{-1 + x_2}{2} = 2 \quad \text{and} \quad \frac{5 + y_2}{2} = 4
\]

Now, solve each equation:

1. For the x-coordinate:
\[
\frac{-1 + x_2}{2} = 2
\]
Multiply both sides by 2:
\[
-1 + x_2 = 4
\]
Add 1 to both sides:
\[
x_2 = 5
\]

2. For the y-coordinate:
\[
\frac{5 + y_2}{2} = 4
\]
Multiply both sides by 2:
\[
5 + y_2 = 8
\]
Subtract 5 from both sides:
\[
y_2 = 3
\]

Thus, the coordinates of point \( B \) are \( (5, 3) \).

Would you like further clarification or details? Here are some related questions:

1. How do we derive the midpoint formula?
2. What is the distance formula for two points?
3. How would you find the slope of the line segment between two points?
4. Can the midpoint formula be used in three dimensions?
5. How does changing one endpoint affect the midpoint?

**Tip:** Always verify your results by plugging the coordinates back into the formula.

The midpoint of line segment 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 a missing point on a line segment using the midpoint formula. This problem involves coordinate geometry and is suitable for students in Grades 6-8. The given midpoint is M(2, 4), and one endpoint is A(-1, 5). Find the coordinates of point B step-by-step.

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